From 169b320ae01a632697b0a5e49a271f8d308bdba1 Mon Sep 17 00:00:00 2001 From: John Stachurski Date: Mon, 3 Aug 2026 15:48:52 +1000 Subject: [PATCH 1/4] Split "Observed Distributions" out of prob_dist and develop it MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Closes #791. `prob_dist.md` was doing two jobs: introducing probability distributions, and working with observed data. This splits the second into its own lecture, sitting immediately after prob_dist in the TOC, and develops the material well past what was there before. Retains the name "Observed Distributions" rather than the "Samples vs Distributions" title floated in the issue. New material in prob_dist: - The standard deviation, which the lecture used in its opening height example without ever defining. - Moments generally — raw, central and standardized — which gives meaning to the "first moment" and "second central moment" language already in the text, then skewness and excess kurtosis as the third and fourth standardized moments. Excess kurtosis (normal = 0) is the headline convention, matching SciPy's default, with a note that some authors do not subtract the 3. - Quantiles, the median, quartiles and the interquartile range. - Worked values via `stats(moments='sk')` and `ppf`, with the lognormal as the contrast case against the normal. The new lecture covers sample moments and sample quantiles, then histograms, empirical distribution functions, kernel density estimates, box-and-whisker plots and violin plots. Three data sets carry it, one per shape: US adult heights (skewness 0.07), Ames house prices (1.74, and about zero in logs), and Japanese deaths by age (-1.60). The mean sits above the median for house prices and below it for age at death, which motivates the quantiles as robust alternatives. Data now comes from QuantEcon/data-lectures per the routing rule in that repo — including us_adult_heights.csv, which moves out of _static/ here (QuantEcon/data-lectures#27). Its builder was recovered in that PR and reproduces the file byte for byte, so the repoint cannot change output. The violin plot link in lln_clt.md is repointed to the new lecture and made a proper cross-reference rather than a hard-coded URL. Co-Authored-By: Claude Opus 5 (1M context) --- .../prob_dist/us_adult_heights.csv | 10479 ---------------- lectures/_static/quant-econ.bib | 9 + lectures/_toc.yml | 1 + lectures/lln_clt.md | 2 +- lectures/observed_distributions.md | 707 ++ lectures/prob_dist.md | 382 +- 6 files changed, 832 insertions(+), 10748 deletions(-) delete mode 100644 lectures/_static/lecture_specific/prob_dist/us_adult_heights.csv create mode 100644 lectures/observed_distributions.md diff --git a/lectures/_static/lecture_specific/prob_dist/us_adult_heights.csv b/lectures/_static/lecture_specific/prob_dist/us_adult_heights.csv deleted file mode 100644 index 3937af8d..00000000 --- a/lectures/_static/lecture_specific/prob_dist/us_adult_heights.csv +++ /dev/null @@ -1,10479 +0,0 @@ -sex,height_cm -male,184.5 -male,171.4 -male,170.1 -male,165.4 -male,179.4 -male,176.7 -male,177.8 -male,183.8 -male,170.7 -male,166.1 -male,170.7 -male,182.2 -male,173.9 -male,187.4 -male,166.3 -male,182.2 -male,178.4 -male,183.7 -male,173.8 -male,165.7 -male,180.3 -male,177.5 -male,170.6 -male,176.4 -male,179.7 -male,172.8 -male,170.6 -male,181.5 -male,189.4 -male,175.6 -male,169.3 -male,169.8 -male,170.0 -male,173.9 -male,167.0 -male,175.9 -male,178.7 -male,173.1 -male,185.4 -male,177.0 -male,188.5 -male,172.4 -male,169.1 -male,178.9 -male,171.6 -male,173.6 -male,170.5 -male,174.0 -male,173.3 -male,166.6 -male,173.0 -male,181.9 -male,172.7 -male,164.1 -male,174.1 -male,176.0 -male,179.4 -male,180.0 -male,169.0 -male,178.1 -male,169.5 -male,176.2 -male,176.5 -male,180.9 -male,178.4 -male,178.4 -male,164.9 -male,182.4 -male,171.5 -male,175.1 -male,173.6 -male,178.2 -male,177.6 -male,167.5 -male,161.4 -male,192.9 -male,169.7 -male,174.6 -male,159.3 -male,171.1 -male,186.5 -male,178.3 -male,161.2 -male,181.8 -male,172.6 -male,176.2 -male,178.9 -male,174.5 -male,164.0 -male,183.3 -male,177.4 -male,169.0 -male,176.8 -male,189.4 -male,166.8 -male,186.5 -male,179.1 -male,165.8 -male,173.2 -male,171.4 -male,165.1 -male,164.2 -male,164.6 -male,154.1 -male,165.2 -male,179.0 -male,154.0 -male,176.7 -male,166.3 -male,156.3 -male,171.6 -male,166.5 -male,182.4 -male,161.0 -male,173.4 -male,174.9 -male,166.2 -male,175.2 -male,149.6 -male,169.2 -male,172.4 -male,167.5 -male,180.1 -male,166.3 -male,176.6 -male,162.0 -male,174.9 -male,167.6 -male,184.0 -male,172.0 -male,163.5 -male,165.7 -male,188.4 -male,173.7 -male,152.4 -male,167.5 -male,163.2 -male,185.1 -male,170.7 -male,178.2 -male,175.4 -male,161.5 -male,162.4 -male,168.5 -male,175.0 -male,177.5 -male,162.3 -male,173.2 -male,174.5 -male,173.7 -male,177.8 -male,177.7 -male,188.1 -male,171.1 -male,190.9 -male,175.6 -male,171.3 -male,174.9 -male,178.8 -male,175.9 -male,155.1 -male,166.3 -male,164.4 -male,172.1 -male,181.0 -male,171.2 -male,171.2 -male,176.6 -male,168.6 -male,169.8 -male,175.1 -male,153.4 -male,188.6 -male,175.3 -male,172.0 -male,160.6 -male,174.5 -male,162.6 -male,179.0 -male,177.2 -male,186.5 -male,182.6 -male,178.3 -male,178.9 -male,166.0 -male,177.1 -male,175.2 -male,182.7 -male,167.8 -male,168.0 -male,163.3 -male,191.8 -male,176.3 -male,177.0 -male,164.0 -male,166.8 -male,178.0 -male,184.4 -male,166.9 -male,174.1 -male,174.7 -male,169.3 -male,171.6 -male,184.4 -male,172.5 -male,165.5 -male,179.7 -male,190.4 -male,177.5 -male,161.9 -male,170.7 -male,172.7 -male,157.2 -male,175.3 -male,198.4 -male,159.9 -male,160.7 -male,177.9 -male,160.8 -male,176.8 -male,169.7 -male,171.6 -male,173.2 -male,167.4 -male,174.5 -male,177.1 -male,180.2 -male,169.4 -male,168.4 -male,181.4 -male,182.7 -male,181.2 -male,169.4 -male,178.9 -male,182.6 -male,161.8 -male,173.1 -male,176.0 -male,170.0 -male,170.8 -male,156.6 -male,169.4 -male,179.0 -male,185.0 -male,167.2 -male,176.1 -male,178.8 -male,182.9 -male,175.9 -male,155.7 -male,185.0 -male,175.7 -male,158.7 -male,163.9 -male,183.5 -male,161.7 -male,162.8 -male,163.3 -male,178.5 -male,166.7 -male,181.3 -male,177.1 -male,168.4 -male,166.4 -male,180.4 -male,177.0 -male,168.5 -male,185.7 -male,189.0 -male,178.0 -male,175.0 -male,177.9 -male,181.3 -male,181.3 -male,174.7 -male,168.0 -male,164.7 -male,170.1 -male,176.7 -male,178.0 -male,163.1 -male,161.0 -male,169.0 -male,163.6 -male,174.5 -male,186.3 -male,177.2 -male,164.7 -male,174.2 -male,186.9 -male,170.8 -male,176.0 -male,178.3 -male,175.5 -male,168.0 -male,191.3 -male,165.1 -male,178.1 -male,159.1 -male,167.4 -male,177.9 -male,173.8 -male,177.6 -male,169.5 -male,190.9 -male,170.4 -male,167.3 -male,175.0 -male,170.1 -male,170.4 -male,182.0 -male,171.2 -male,159.3 -male,179.3 -male,179.0 -male,149.4 -male,180.4 -male,171.6 -male,174.1 -male,175.9 -male,164.7 -male,174.3 -male,181.4 -male,159.0 -male,182.3 -male,170.9 -male,182.2 -male,167.0 -male,169.2 -male,183.6 -male,178.1 -male,193.3 -male,173.9 -male,186.6 -male,169.1 -male,163.9 -male,172.9 -male,179.2 -male,182.6 -male,182.3 -male,179.5 -male,177.3 -male,170.6 -male,186.8 -male,164.4 -male,180.9 -male,183.5 -male,161.8 -male,176.1 -male,171.5 -male,159.6 -male,171.5 -male,175.3 -male,169.6 -male,170.3 -male,163.1 -male,172.5 -male,181.3 -male,170.2 -male,173.0 -male,167.4 -male,174.0 -male,171.6 -male,166.7 -male,170.8 -male,167.3 -male,170.9 -male,190.2 -male,174.2 -male,178.2 -male,166.8 -male,169.7 -male,178.4 -male,177.5 -male,159.8 -male,169.0 -male,169.4 -male,177.8 -male,180.7 -male,163.6 -male,177.7 -male,178.2 -male,171.9 -male,163.6 -male,179.0 -male,167.7 -male,158.3 -male,167.9 -male,171.2 -male,166.9 -male,158.4 -male,169.2 -male,174.1 -male,169.9 -male,171.9 -male,174.2 -male,183.6 -male,177.4 -male,166.4 -male,172.7 -male,167.0 -male,176.4 -male,169.7 -male,177.2 -male,177.2 -male,172.5 -male,183.9 -male,180.8 -male,184.2 -male,175.8 -male,166.3 -male,172.8 -male,173.6 -male,180.9 -male,176.4 -male,178.5 -male,184.8 -male,169.2 -male,184.9 -male,173.8 -male,181.8 -male,163.1 -male,184.5 -male,168.4 -male,164.6 -male,167.6 -male,165.5 -male,177.6 -male,180.6 -male,178.0 -male,178.7 -male,176.0 -male,171.0 -male,163.9 -male,177.9 -male,168.9 -male,170.2 -male,159.6 -male,171.9 -male,171.0 -male,176.7 -male,163.4 -male,172.4 -male,158.9 -male,172.7 -male,172.5 -male,169.2 -male,162.5 -male,170.9 -male,161.8 -male,179.2 -male,183.4 -male,163.5 -male,175.5 -male,181.5 -male,162.6 -male,170.3 -male,178.1 -male,164.6 -male,160.1 -male,188.5 -male,165.7 -male,175.9 -male,167.9 -male,179.4 -male,168.3 -male,185.0 -male,173.6 -male,193.2 -male,171.9 -male,166.9 -male,175.5 -male,174.2 -male,172.5 -male,179.5 -male,179.0 -male,172.0 -male,169.0 -male,170.7 -male,163.8 -male,181.1 -male,169.0 -male,171.2 -male,179.1 -male,173.9 -male,160.7 -male,178.5 -male,174.4 -male,172.3 -male,181.3 -male,167.0 -male,183.8 -male,184.8 -male,175.1 -male,186.6 -male,173.9 -male,171.6 -male,174.9 -male,163.7 -male,172.8 -male,171.9 -male,174.9 -male,172.0 -male,175.8 -male,179.6 -male,177.9 -male,183.9 -male,179.2 -male,183.4 -male,186.1 -male,176.2 -male,164.5 -male,166.8 -male,171.6 -male,171.0 -male,162.6 -male,169.3 -male,170.4 -male,177.3 -male,173.7 -male,179.4 -male,173.9 -male,180.5 -male,164.3 -male,175.9 -male,157.3 -male,168.5 -male,193.1 -male,164.7 -male,169.5 -male,169.7 -male,171.3 -male,172.9 -male,185.3 -male,188.3 -male,172.0 -male,184.3 -male,189.0 -male,167.9 -male,174.0 -male,186.5 -male,176.0 -male,175.0 -male,179.3 -male,164.9 -male,170.8 -male,166.8 -male,171.0 -male,164.1 -male,188.0 -male,167.7 -male,177.6 -male,166.4 -male,171.9 -male,177.3 -male,153.1 -male,171.1 -male,169.6 -male,164.8 -male,176.6 -male,173.4 -male,175.7 -male,170.0 -male,161.9 -male,170.6 -male,171.8 -male,183.0 -male,183.2 -male,173.5 -male,178.2 -male,176.9 -male,161.7 -male,162.5 -male,165.0 -male,177.1 -male,165.6 -male,171.6 -male,177.4 -male,170.3 -male,179.0 -male,174.2 -male,184.4 -male,183.7 -male,173.5 -male,174.1 -male,187.3 -male,176.5 -male,159.0 -male,179.6 -male,168.2 -male,158.2 -male,174.8 -male,178.8 -male,175.9 -male,156.4 -male,175.4 -male,173.8 -male,178.7 -male,176.4 -male,164.8 -male,176.9 -male,176.7 -male,167.8 -male,179.0 -male,170.8 -male,166.6 -male,169.8 -male,177.9 -male,179.8 -male,167.9 -male,169.0 -male,159.9 -male,171.8 -male,173.6 -male,171.6 -male,181.5 -male,185.8 -male,177.8 -male,166.4 -male,176.8 -male,165.7 -male,162.5 -male,178.5 -male,162.6 -male,168.0 -male,177.9 -male,187.7 -male,172.8 -male,159.3 -male,169.4 -male,172.4 -male,178.3 -male,168.5 -male,180.3 -male,166.7 -male,175.1 -male,178.4 -male,168.0 -male,174.2 -male,160.6 -male,173.5 -male,158.9 -male,173.9 -male,182.3 -male,160.1 -male,165.0 -male,157.2 -male,178.9 -male,176.5 -male,173.4 -male,166.6 -male,163.1 -male,175.6 -male,182.0 -male,180.4 -male,173.1 -male,171.7 -male,169.3 -male,176.8 -male,165.6 -male,172.8 -male,177.3 -male,168.3 -male,178.5 -male,172.9 -male,166.9 -male,175.2 -male,164.0 -male,150.8 -male,174.1 -male,168.5 -male,159.1 -male,180.5 -male,160.7 -male,187.4 -male,179.0 -male,173.4 -male,166.8 -male,171.3 -male,177.6 -male,176.4 -male,179.6 -male,169.5 -male,161.2 -male,161.5 -male,174.1 -male,168.7 -male,166.5 -male,173.3 -male,174.3 -male,164.2 -male,163.5 -male,179.3 -male,189.9 -male,157.9 -male,172.2 -male,182.7 -male,178.7 -male,170.1 -male,156.6 -male,179.3 -male,172.6 -male,175.0 -male,171.5 -male,174.7 -male,165.7 -male,171.9 -male,169.6 -male,178.1 -male,162.0 -male,175.0 -male,168.9 -male,162.2 -male,171.5 -male,158.0 -male,158.1 -male,195.1 -male,180.0 -male,172.0 -male,161.1 -male,163.8 -male,171.8 -male,167.1 -male,158.9 -male,158.8 -male,171.6 -male,201.0 -male,172.9 -male,180.1 -male,176.3 -male,171.3 -male,162.4 -male,173.6 -male,157.3 -male,173.8 -male,166.9 -male,165.0 -male,177.7 -male,157.0 -male,168.4 -male,174.2 -male,167.9 -male,180.8 -male,183.9 -male,172.5 -male,169.2 -male,168.7 -male,180.1 -male,175.4 -male,178.9 -male,171.3 -male,163.5 -male,173.2 -male,178.3 -male,179.0 -male,187.2 -male,184.2 -male,178.4 -male,174.9 -male,171.1 -male,169.3 -male,169.7 -male,175.4 -male,192.1 -male,178.9 -male,182.5 -male,173.1 -male,179.2 -male,162.3 -male,172.0 -male,182.5 -male,181.7 -male,160.8 -male,177.1 -male,174.0 -male,155.0 -male,165.3 -male,179.6 -male,172.4 -male,176.0 -male,178.8 -male,161.6 -male,157.7 -male,168.4 -male,174.4 -male,171.0 -male,149.8 -male,191.8 -male,173.8 -male,166.1 -male,169.9 -male,179.1 -male,168.8 -male,164.8 -male,174.2 -male,174.1 -male,168.1 -male,174.2 -male,159.8 -male,173.7 -male,172.4 -male,174.1 -male,168.7 -male,173.2 -male,161.8 -male,163.4 -male,162.5 -male,172.9 -male,176.9 -male,176.5 -male,157.7 -male,172.8 -male,170.7 -male,180.3 -male,174.6 -male,173.4 -male,170.6 -male,171.3 -male,165.3 -male,180.5 -male,169.2 -male,186.4 -male,178.1 -male,168.7 -male,175.7 -male,178.1 -male,178.8 -male,156.2 -male,176.7 -male,172.7 -male,173.5 -male,170.8 -male,171.9 -male,165.3 -male,165.0 -male,164.0 -male,160.7 -male,173.5 -male,168.7 -male,164.7 -male,158.0 -male,184.8 -male,178.1 -male,161.2 -male,180.0 -male,175.4 -male,178.9 -male,184.6 -male,178.7 -male,157.0 -male,168.9 -male,169.2 -male,171.8 -male,182.3 -male,178.6 -male,174.6 -male,159.5 -male,168.2 -male,180.7 -male,169.9 -male,179.9 -male,167.4 -male,174.7 -male,166.4 -male,168.4 -male,180.9 -male,169.5 -male,163.5 -male,175.7 -male,158.8 -male,184.5 -male,163.4 -male,178.0 -male,167.0 -male,177.6 -male,182.3 -male,161.4 -male,168.2 -male,177.8 -male,184.7 -male,180.4 -male,163.3 -male,172.4 -male,181.3 -male,167.6 -male,170.0 -male,187.3 -male,174.6 -male,181.7 -male,177.8 -male,170.6 -male,172.9 -male,165.2 -male,169.5 -male,171.5 -male,178.2 -male,166.6 -male,174.9 -male,163.6 -male,170.2 -male,171.6 -male,183.4 -male,172.2 -male,166.6 -male,159.3 -male,179.3 -male,165.6 -male,174.2 -male,162.7 -male,159.0 -male,170.8 -male,177.2 -male,176.9 -male,178.9 -male,179.1 -male,185.3 -male,161.3 -male,176.9 -male,180.5 -male,164.5 -male,156.8 -male,170.7 -male,176.6 -male,191.9 -male,168.0 -male,179.7 -male,183.5 -male,163.7 -male,174.5 -male,171.0 -male,170.4 -male,161.2 -male,176.4 -male,174.0 -male,171.9 -male,174.9 -male,173.5 -male,172.8 -male,172.3 -male,167.6 -male,169.2 -male,181.8 -male,178.9 -male,179.1 -male,185.0 -male,189.3 -male,169.8 -male,159.5 -male,176.3 -male,148.8 -male,175.3 -male,181.1 -male,165.9 -male,169.4 -male,180.3 -male,187.4 -male,162.7 -male,176.6 -male,165.3 -male,177.5 -male,163.3 -male,166.9 -male,165.2 -male,175.0 -male,182.7 -male,167.9 -male,176.9 -male,176.2 -male,179.3 -male,175.2 -male,172.6 -male,162.7 -male,189.4 -male,173.8 -male,156.1 -male,173.3 -male,178.9 -male,168.3 -male,178.5 -male,173.0 -male,178.5 -male,177.8 -male,181.4 -male,177.1 -male,181.5 -male,167.5 -male,162.1 -male,173.3 -male,163.3 -male,172.0 -male,172.7 -male,172.3 -male,184.0 -male,181.1 -male,161.0 -male,176.8 -male,172.9 -male,171.8 -male,181.5 -male,150.6 -male,163.1 -male,173.7 -male,166.9 -male,163.3 -male,167.5 -male,157.0 -male,180.2 -male,177.0 -male,177.3 -male,152.8 -male,175.2 -male,179.6 -male,172.2 -male,159.1 -male,194.3 -male,170.7 -male,181.4 -male,188.9 -male,169.3 -male,166.7 -male,184.5 -male,165.0 -male,187.3 -male,161.1 -male,171.3 -male,175.2 -male,175.1 -male,177.5 -male,168.4 -male,172.2 -male,171.2 -male,172.8 -male,189.2 -male,174.3 -male,165.7 -male,182.6 -male,165.2 -male,161.1 -male,169.8 -male,187.1 -male,161.6 -male,171.3 -male,172.2 -male,172.9 -male,167.2 -male,182.3 -male,175.9 -male,170.0 -male,171.4 -male,166.5 -male,168.0 -male,164.7 -male,174.9 -male,180.4 -male,176.8 -male,182.0 -male,184.9 -male,175.2 -male,176.6 -male,178.2 -male,168.7 -male,168.4 -male,173.3 -male,179.7 -male,170.4 -male,170.7 -male,168.2 -male,167.9 -male,171.6 -male,167.9 -male,184.0 -male,182.6 -male,177.2 -male,177.5 -male,177.0 -male,167.6 -male,175.0 -male,166.2 -male,180.0 -male,182.0 -male,189.9 -male,178.5 -male,169.9 -male,172.9 -male,177.0 -male,169.4 -male,174.1 -male,176.6 -male,155.4 -male,169.5 -male,167.0 -male,162.9 -male,182.3 -male,164.9 -male,182.9 -male,176.9 -male,166.6 -male,182.8 -male,177.8 -male,172.2 -male,183.4 -male,176.6 -male,159.6 -male,181.7 -male,180.6 -male,183.1 -male,176.1 -male,174.9 -male,175.3 -male,168.4 -male,187.8 -male,170.3 -male,172.5 -male,176.8 -male,174.4 -male,186.2 -male,167.7 -male,178.6 -male,165.1 -male,189.4 -male,178.8 -male,184.4 -male,175.4 -male,169.0 -male,178.9 -male,177.0 -male,165.8 -male,187.4 -male,169.2 -male,176.1 -male,175.6 -male,174.7 -male,176.0 -male,167.3 -male,170.0 -male,178.5 -male,176.7 -male,166.0 -male,176.0 -male,164.8 -male,172.9 -male,181.1 -male,172.7 -male,169.8 -male,165.7 -male,164.5 -male,164.1 -male,169.3 -male,202.7 -male,175.9 -male,174.7 -male,179.7 -male,181.3 -male,178.0 -male,178.8 -male,169.7 -male,167.7 -male,169.9 -male,169.6 -male,161.7 -male,165.5 -male,162.6 -male,185.8 -male,178.5 -male,175.9 -male,180.5 -male,175.4 -male,164.1 -male,176.3 -male,174.0 -male,168.1 -male,171.3 -male,178.1 -male,172.2 -male,174.3 -male,167.3 -male,176.7 -male,178.5 -male,179.5 -male,175.5 -male,170.8 -male,177.5 -male,170.0 -male,180.8 -male,157.4 -male,165.7 -male,168.6 -male,173.8 -male,177.1 -male,161.6 -male,169.0 -male,166.4 -male,161.7 -male,176.2 -male,158.2 -male,174.8 -male,169.2 -male,163.8 -male,170.1 -male,179.1 -male,172.1 -male,168.4 -male,171.8 -male,169.1 -male,175.2 -male,165.6 -male,187.4 -male,178.5 -male,158.3 -male,175.5 -male,174.2 -male,180.5 -male,174.5 -male,175.5 -male,178.1 -male,179.1 -male,165.4 -male,174.6 -male,169.6 -male,173.6 -male,170.3 -male,171.9 -male,162.4 -male,162.4 -male,167.2 -male,159.2 -male,163.9 -male,182.7 -male,169.7 -male,172.8 -male,164.7 -male,174.1 -male,175.5 -male,169.1 -male,178.2 -male,173.7 -male,164.2 -male,166.0 -male,166.8 -male,169.2 -male,176.8 -male,172.1 -male,173.9 -male,184.2 -male,174.9 -male,168.1 -male,176.6 -male,167.0 -male,169.0 -male,182.6 -male,173.1 -male,174.3 -male,178.4 -male,159.2 -male,175.4 -male,182.9 -male,160.9 -male,173.8 -male,158.4 -male,178.4 -male,168.1 -male,179.9 -male,170.5 -male,183.4 -male,164.2 -male,173.4 -male,172.8 -male,183.8 -male,181.7 -male,180.4 -male,171.2 -male,168.9 -male,171.0 -male,170.8 -male,174.2 -male,168.4 -male,182.8 -male,179.9 -male,166.2 -male,162.6 -male,165.6 -male,176.6 -male,177.5 -male,161.7 -male,168.3 -male,166.9 -male,176.9 -male,162.4 -male,177.3 -male,166.3 -male,167.4 -male,171.1 -male,176.8 -male,174.4 -male,173.6 -male,185.0 -male,182.5 -male,180.7 -male,171.9 -male,195.6 -male,177.8 -male,183.6 -male,188.5 -male,156.8 -male,169.6 -male,168.6 -male,176.7 -male,158.6 -male,168.4 -male,177.7 -male,172.8 -male,162.0 -male,172.9 -male,165.1 -male,173.7 -male,161.3 -male,175.1 -male,173.2 -male,170.0 -male,181.3 -male,163.2 -male,152.3 -male,185.3 -male,161.1 -male,181.8 -male,169.5 -male,178.2 -male,170.5 -male,176.0 -male,175.0 -male,173.6 -male,170.5 -male,176.4 -male,175.2 -male,176.4 -male,175.8 -male,157.2 -male,173.3 -male,163.2 -male,157.0 -male,170.5 -male,178.6 -male,160.4 -male,167.4 -male,173.3 -male,175.3 -male,185.3 -male,184.8 -male,174.0 -male,174.9 -male,182.9 -male,170.2 -male,180.7 -male,169.1 -male,176.8 -male,166.1 -male,185.1 -male,171.9 -male,173.6 -male,184.2 -male,173.3 -male,173.6 -male,164.9 -male,188.1 -male,162.3 -male,177.2 -male,161.2 -male,168.7 -male,184.2 -male,178.9 -male,174.7 -male,172.1 -male,183.0 -male,161.0 -male,185.6 -male,165.9 -male,174.0 -male,177.0 -male,173.5 -male,167.8 -male,170.6 -male,182.3 -male,172.5 -male,177.3 -male,175.8 -male,169.4 -male,157.0 -male,178.8 -male,177.5 -male,171.1 -male,159.9 -male,186.7 -male,178.6 -male,178.9 -male,183.3 -male,170.1 -male,179.6 -male,169.1 -male,175.3 -male,165.4 -male,167.7 -male,170.1 -male,172.2 -male,173.6 -male,173.7 -male,174.1 -male,173.4 -male,172.8 -male,170.6 -male,179.3 -male,170.3 -male,167.1 -male,175.8 -male,185.3 -male,174.0 -male,178.3 -male,173.7 -male,180.1 -male,187.5 -male,184.0 -male,177.7 -male,175.1 -male,177.2 -male,159.4 -male,181.6 -male,178.0 -male,161.1 -male,180.2 -male,167.9 -male,172.9 -male,176.1 -male,171.4 -male,171.3 -male,181.6 -male,171.5 -male,170.4 -male,170.4 -male,170.3 -male,181.7 -male,181.0 -male,179.1 -male,179.6 -male,170.4 -male,177.2 -male,152.9 -male,174.9 -male,158.6 -male,174.5 -male,174.5 -male,178.1 -male,184.5 -male,174.5 -male,171.8 -male,188.4 -male,161.0 -male,185.0 -male,184.2 -male,181.8 -male,169.1 -male,181.8 -male,167.1 -male,177.2 -male,169.7 -male,166.7 -male,178.7 -male,192.9 -male,178.3 -male,177.0 -male,175.6 -male,169.7 -male,165.1 -male,175.9 -male,177.6 -male,174.0 -male,169.0 -male,171.8 -male,162.0 -male,169.6 -male,166.5 -male,170.5 -male,183.4 -male,164.7 -male,173.2 -male,177.3 -male,166.3 -male,177.6 -male,167.9 -male,175.0 -male,183.1 -male,166.8 -male,163.3 -male,154.0 -male,184.8 -male,172.6 -male,181.4 -male,185.3 -male,187.7 -male,168.8 -male,172.6 -male,182.7 -male,173.4 -male,166.5 -male,169.9 -male,177.9 -male,173.1 -male,183.0 -male,158.5 -male,164.5 -male,157.1 -male,169.9 -male,185.7 -male,182.3 -male,181.0 -male,182.8 -male,180.5 -male,168.0 -male,179.7 -male,171.1 -male,163.6 -male,180.5 -male,164.3 -male,183.6 -male,172.0 -male,167.1 -male,178.2 -male,154.1 -male,175.7 -male,182.6 -male,166.8 -male,179.1 -male,178.9 -male,180.0 -male,152.8 -male,172.7 -male,172.3 -male,171.0 -male,180.1 -male,181.8 -male,180.4 -male,177.9 -male,170.1 -male,170.4 -male,187.0 -male,179.6 -male,178.5 -male,177.7 -male,188.6 -male,181.0 -male,181.7 -male,166.5 -male,165.9 -male,161.7 -male,178.9 -male,167.1 -male,173.5 -male,190.3 -male,173.5 -male,185.6 -male,177.9 -male,168.6 -male,173.4 -male,166.2 -male,175.3 -male,180.7 -male,173.4 -male,168.0 -male,187.7 -male,176.8 -male,161.1 -male,167.2 -male,171.2 -male,178.5 -male,165.0 -male,175.9 -male,175.4 -male,183.0 -male,175.7 -male,169.3 -male,169.8 -male,170.5 -male,165.9 -male,165.3 -male,175.4 -male,170.0 -male,186.7 -male,177.6 -male,166.8 -male,161.0 -male,156.6 -male,174.4 -male,189.7 -male,176.2 -male,180.4 -male,162.6 -male,192.1 -male,181.8 -male,181.2 -male,180.2 -male,177.1 -male,181.6 -male,159.5 -male,159.3 -male,182.5 -male,173.9 -male,165.8 -male,174.1 -male,185.2 -male,174.3 -male,163.1 -male,170.9 -male,181.7 -male,175.3 -male,169.3 -male,171.4 -male,184.4 -male,182.4 -male,161.1 -male,175.4 -male,171.5 -male,168.3 -male,183.8 -male,177.8 -male,174.1 -male,176.2 -male,187.9 -male,183.9 -male,178.1 -male,173.0 -male,168.4 -male,166.4 -male,182.6 -male,181.0 -male,188.3 -male,166.5 -male,175.5 -male,181.6 -male,183.5 -male,168.2 -male,171.9 -male,167.2 -male,168.4 -male,185.1 -male,183.1 -male,174.0 -male,175.5 -male,161.4 -male,154.7 -male,186.1 -male,169.0 -male,163.0 -male,170.6 -male,165.5 -male,165.2 -male,181.4 -male,188.0 -male,173.7 -male,170.5 -male,179.8 -male,193.5 -male,162.7 -male,176.9 -male,178.7 -male,169.2 -male,175.1 -male,179.0 -male,174.4 -male,175.9 -male,172.0 -male,169.6 -male,171.3 -male,175.1 -male,154.8 -male,171.1 -male,179.3 -male,160.4 -male,161.9 -male,175.0 -male,175.2 -male,164.5 -male,166.7 -male,179.9 -male,175.1 -male,172.6 -male,177.6 -male,172.5 -male,177.4 -male,175.3 -male,166.2 -male,175.2 -male,160.9 -male,173.2 -male,173.6 -male,172.0 -male,183.2 -male,171.6 -male,183.5 -male,175.5 -male,174.1 -male,175.3 -male,159.1 -male,182.1 -male,171.3 -male,169.6 -male,174.6 -male,170.0 -male,160.6 -male,178.3 -male,171.2 -male,173.6 -male,176.2 -male,174.1 -male,169.5 -male,148.8 -male,140.1 -male,189.9 -male,176.5 -male,165.9 -male,175.8 -male,167.6 -male,176.5 -male,166.7 -male,171.6 -male,164.8 -male,168.8 -male,169.4 -male,167.4 -male,168.6 -male,180.1 -male,163.6 -male,179.3 -male,173.0 -male,177.1 -male,158.5 -male,172.1 -male,186.2 -male,193.8 -male,180.1 -male,178.9 -male,160.3 -male,178.2 -male,176.2 -male,166.7 -male,173.5 -male,174.1 -male,151.8 -male,169.9 -male,160.3 -male,163.2 -male,177.6 -male,168.4 -male,176.1 -male,178.6 -male,177.8 -male,176.4 -male,172.1 -male,167.3 -male,177.5 -male,181.7 -male,167.8 -male,176.0 -male,177.4 -male,166.1 -male,169.5 -male,174.8 -male,171.1 -male,178.2 -male,183.5 -male,170.4 -male,162.7 -male,159.7 -male,166.1 -male,168.8 -male,177.5 -male,181.8 -male,185.7 -male,153.5 -male,174.2 -male,160.8 -male,180.7 -male,164.7 -male,161.2 -male,176.0 -male,180.4 -male,169.8 -male,166.2 -male,178.9 -male,158.7 -male,170.0 -male,180.0 -male,178.7 -male,167.6 -male,169.6 -male,179.9 -male,185.3 -male,161.3 -male,177.8 -male,171.4 -male,178.0 -male,174.5 -male,164.3 -male,172.1 -male,163.4 -male,177.9 -male,177.8 -male,167.3 -male,188.3 -male,177.4 -male,170.1 -male,174.6 -male,175.0 -male,170.7 -male,178.9 -male,174.5 -male,175.0 -male,173.9 -male,165.2 -male,184.6 -male,171.0 -male,174.6 -male,189.8 -male,181.6 -male,167.1 -male,177.9 -male,174.0 -male,172.9 -male,171.1 -male,167.3 -male,178.0 -male,173.3 -male,169.6 -male,172.4 -male,173.9 -male,173.9 -male,182.2 -male,162.8 -male,181.4 -male,171.3 -male,170.5 -male,170.5 -male,178.1 -male,172.2 -male,177.3 -male,168.2 -male,184.9 -male,174.4 -male,175.8 -male,179.2 -male,170.2 -male,182.2 -male,171.6 -male,171.0 -male,176.0 -male,175.6 -male,165.3 -male,195.4 -male,171.5 -male,166.8 -male,168.1 -male,178.0 -male,183.2 -male,171.9 -male,183.8 -male,171.5 -male,180.2 -male,170.7 -male,177.4 -male,166.4 -male,177.0 -male,172.5 -male,162.8 -male,173.3 -male,174.6 -male,176.3 -male,167.2 -male,194.6 -male,178.5 -male,184.8 -male,172.9 -male,169.6 -male,170.4 -male,178.5 -male,179.4 -male,170.3 -male,162.5 -male,153.6 -male,169.6 -male,167.2 -male,182.4 -male,167.6 -male,180.2 -male,171.2 -male,184.7 -male,173.1 -male,150.4 -male,176.8 -male,181.6 -male,170.5 -male,172.0 -male,167.7 -male,174.3 -male,166.2 -male,167.6 -male,171.5 -male,174.6 -male,171.0 -male,163.5 -male,159.9 -male,184.7 -male,172.4 -male,166.3 -male,169.6 -male,172.8 -male,165.9 -male,170.9 -male,166.9 -male,180.8 -male,185.5 -male,172.7 -male,168.4 -male,183.8 -male,181.3 -male,174.6 -male,166.5 -male,183.3 -male,168.1 -male,169.0 -male,168.9 -male,173.3 -male,175.4 -male,182.4 -male,172.4 -male,168.5 -male,170.9 -male,164.5 -male,164.9 -male,180.6 -male,177.6 -male,179.6 -male,171.8 -male,173.1 -male,186.8 -male,161.0 -male,169.3 -male,176.1 -male,173.8 -male,172.2 -male,164.7 -male,169.4 -male,178.6 -male,170.0 -male,179.5 -male,169.8 -male,165.7 -male,173.3 -male,170.2 -male,171.0 -male,177.2 -male,166.6 -male,174.8 -male,173.7 -male,169.2 -male,154.0 -male,176.0 -male,162.4 -male,175.7 -male,183.5 -male,176.7 -male,184.0 -male,169.7 -male,166.0 -male,171.6 -male,183.6 -male,167.7 -male,157.3 -male,174.8 -male,177.1 -male,162.4 -male,165.6 -male,172.3 -male,158.7 -male,181.7 -male,177.4 -male,176.6 -male,169.9 -male,170.9 -male,174.0 -male,180.4 -male,183.0 -male,178.6 -male,174.2 -male,174.2 -male,166.9 -male,171.2 -male,175.7 -male,176.0 -male,161.3 -male,182.6 -male,180.1 -male,179.7 -male,178.0 -male,178.4 -male,191.2 -male,171.2 -male,182.4 -male,162.9 -male,179.3 -male,170.4 -male,174.6 -male,175.5 -male,174.8 -male,181.5 -male,191.1 -male,163.1 -male,169.6 -male,157.1 -male,180.9 -male,168.1 -male,167.7 -male,154.8 -male,187.6 -male,186.8 -male,176.9 -male,174.1 -male,165.6 -male,171.7 -male,157.1 -male,169.0 -male,170.2 -male,182.5 -male,174.0 -male,183.5 -male,169.1 -male,172.4 -male,172.8 -male,163.2 -male,171.6 -male,168.5 -male,176.4 -male,174.9 -male,169.2 -male,178.2 -male,168.6 -male,161.6 -male,173.0 -male,168.4 -male,168.5 -male,176.9 -male,171.5 -male,167.7 -male,186.3 -male,169.4 -male,167.9 -male,173.6 -male,161.5 -male,178.4 -male,169.5 -male,177.4 -male,180.1 -male,172.5 -male,169.0 -male,167.3 -male,181.7 -male,184.3 -male,164.0 -male,180.7 -male,179.6 -male,171.6 -male,169.8 -male,183.2 -male,167.9 -male,178.9 -male,176.3 -male,175.1 -male,180.1 -male,167.7 -male,175.2 -male,180.5 -male,179.6 -male,176.9 -male,166.8 -male,159.5 -male,178.2 -male,167.0 -male,159.7 -male,183.6 -male,167.3 -male,162.3 -male,165.5 -male,161.4 -male,170.1 -male,175.7 -male,182.0 -male,171.4 -male,179.7 -male,177.4 -male,177.3 -male,188.1 -male,176.6 -male,171.2 -male,172.5 -male,173.4 -male,169.0 -male,182.8 -male,172.1 -male,188.8 -male,175.3 -male,182.1 -male,180.2 -male,163.4 -male,178.3 -male,184.9 -male,171.4 -male,168.9 -male,162.2 -male,179.7 -male,164.7 -male,167.8 -male,150.8 -male,178.1 -male,178.2 -male,183.1 -male,167.1 -male,177.4 -male,167.2 -male,182.5 -male,169.6 -male,177.7 -male,179.7 -male,177.9 -male,173.4 -male,160.6 -male,184.0 -male,164.0 -male,179.6 -male,175.9 -male,175.4 -male,172.8 -male,179.9 -male,161.7 -male,152.8 -male,180.0 -male,172.3 -male,171.8 -male,167.4 -male,176.2 -male,179.7 -male,183.7 -male,173.9 -male,181.2 -male,171.9 -male,166.7 -male,156.5 -male,173.2 -male,165.9 -male,187.9 -male,178.6 -male,174.2 -male,168.6 -male,176.9 -male,160.5 -male,167.5 -male,154.3 -male,175.5 -male,158.6 -male,170.3 -male,183.4 -male,176.3 -male,174.9 -male,185.7 -male,181.6 -male,168.4 -male,173.7 -male,171.0 -male,176.0 -male,173.9 -male,166.4 -male,190.8 -male,169.6 -male,184.1 -male,187.9 -male,183.5 -male,159.1 -male,181.0 -male,176.1 -male,169.7 -male,176.4 -male,172.8 -male,176.9 -male,165.4 -male,172.0 -male,179.0 -male,164.9 -male,179.3 -male,182.1 -male,177.1 -male,185.2 -male,168.6 -male,175.5 -male,172.6 -male,178.3 -male,164.3 -male,173.1 -male,168.0 -male,167.2 -male,172.3 -male,181.0 -male,151.5 -male,179.0 -male,166.8 -male,173.8 -male,175.5 -male,168.6 -male,180.3 -male,178.4 -male,172.0 -male,166.5 -male,149.2 -male,170.5 -male,176.5 -male,178.8 -male,172.1 -male,174.8 -male,173.0 -male,168.7 -male,155.6 -male,171.5 -male,175.5 -male,166.0 -male,161.7 -male,181.9 -male,179.4 -male,166.4 -male,164.2 -male,174.0 -male,178.7 -male,175.6 -male,178.6 -male,164.4 -male,169.6 -male,179.5 -male,164.1 -male,180.3 -male,174.5 -male,171.7 -male,185.3 -male,168.8 -male,170.5 -male,150.7 -male,157.0 -male,177.2 -male,168.0 -male,171.0 -male,179.4 -male,174.6 -male,185.8 -male,167.7 -male,176.0 -male,184.1 -male,163.6 -male,162.0 -male,170.3 -male,175.3 -male,185.4 -male,173.9 -male,183.1 -male,168.2 -male,176.2 -male,163.2 -male,187.2 -male,169.0 -male,182.2 -male,173.3 -male,183.6 -male,180.3 -male,169.2 -male,164.6 -male,189.4 -male,165.7 -male,184.8 -male,164.4 -male,154.7 -male,188.6 -male,166.6 -male,182.3 -male,161.4 -male,159.1 -male,170.3 -male,166.5 -male,183.7 -male,174.5 -male,177.2 -male,170.6 -male,164.0 -male,167.6 -male,169.1 -male,174.9 -male,161.0 -male,160.5 -male,172.1 -male,156.9 -male,171.0 -male,168.1 -male,177.6 -male,172.9 -male,167.9 -male,166.3 -male,174.6 -male,156.4 -male,167.2 -male,169.1 -male,174.5 -male,167.6 -male,175.4 -male,179.5 -male,172.7 -male,182.1 -male,169.6 -male,175.9 -male,154.4 -male,168.7 -male,164.3 -male,188.1 -male,177.1 -male,189.1 -male,181.4 -male,178.6 -male,172.2 -male,178.7 -male,185.0 -male,179.4 -male,180.1 -male,174.6 -male,174.8 -male,178.0 -male,174.8 -male,182.3 -male,182.6 -male,173.9 -male,187.5 -male,171.5 -male,184.1 -male,171.2 -male,174.2 -male,176.3 -male,173.6 -male,177.4 -male,178.2 -male,179.6 -male,171.9 -male,179.0 -male,156.4 -male,178.6 -male,179.3 -male,175.1 -male,184.7 -male,179.9 -male,168.0 -male,176.5 -male,167.1 -male,184.1 -male,171.7 -male,177.1 -male,173.5 -male,180.2 -male,193.6 -male,169.7 -male,173.1 -male,157.5 -male,167.4 -male,180.2 -male,172.0 -male,166.9 -male,183.6 -male,177.7 -male,169.6 -male,185.8 -male,173.6 -male,169.4 -male,165.7 -male,172.8 -male,182.1 -male,172.2 -male,178.6 -male,163.1 -male,164.1 -male,170.4 -male,170.5 -male,163.2 -male,166.3 -male,178.4 -male,176.8 -male,168.3 -male,167.8 -male,180.3 -male,183.1 -male,166.5 -male,168.8 -male,182.6 -male,175.0 -male,179.5 -male,172.3 -male,175.0 -male,167.3 -male,169.4 -male,174.8 -male,168.1 -male,181.3 -male,154.9 -male,174.4 -male,164.1 -male,167.7 -male,175.9 -male,179.3 -male,175.2 -male,163.8 -male,179.8 -male,179.6 -male,172.8 -male,185.5 -male,166.2 -male,175.0 -male,171.4 -male,179.1 -male,169.6 -male,185.6 -male,158.0 -male,179.7 -male,168.5 -male,175.7 -male,173.3 -male,165.5 -male,184.2 -male,171.6 -male,165.2 -male,163.8 -male,168.5 -male,180.3 -male,182.0 -male,173.4 -male,178.1 -male,167.8 -male,177.8 -male,175.9 -male,175.0 -male,159.6 -male,188.4 -male,170.8 -male,181.4 -male,178.4 -male,163.3 -male,163.6 -male,171.6 -male,162.3 -male,176.1 -male,159.6 -male,176.3 -male,174.2 -male,178.0 -male,176.9 -male,169.3 -male,174.8 -male,164.3 -male,179.0 -male,177.3 -male,160.2 -male,168.0 -male,175.4 -male,179.3 -male,164.1 -male,165.6 -male,166.4 -male,168.9 -male,165.2 -male,182.7 -male,180.2 -male,173.3 -male,170.3 -male,159.4 -male,172.9 -male,173.4 -male,172.9 -male,168.5 -male,173.0 -male,175.6 -male,166.3 -male,168.6 -male,176.2 -male,185.1 -male,163.2 -male,159.7 -male,179.9 -male,191.3 -male,172.2 -male,170.8 -male,175.9 -male,170.6 -male,173.7 -male,192.4 -male,175.0 -male,169.1 -male,170.1 -male,169.8 -male,187.4 -male,161.2 -male,180.9 -male,171.9 -male,191.7 -male,164.8 -male,163.4 -male,187.8 -male,180.4 -male,162.9 -male,168.0 -male,184.6 -male,154.3 -male,170.4 -male,175.2 -male,177.3 -male,175.5 -male,168.6 -male,165.0 -male,161.9 -male,156.1 -male,155.8 -male,182.0 -male,184.6 -male,183.8 -male,172.1 -male,164.0 -male,178.8 -male,176.2 -male,176.8 -male,176.5 -male,169.5 -male,183.0 -male,178.3 -male,172.1 -male,179.5 -male,169.3 -male,155.1 -male,164.5 -male,182.9 -male,187.1 -male,161.1 -male,180.6 -male,183.1 -male,165.2 -male,180.5 -male,175.4 -male,167.0 -male,177.7 -male,177.9 -male,170.7 -male,175.1 -male,175.7 -male,178.4 -male,178.4 -male,193.7 -male,181.8 -male,172.1 -male,168.4 -male,170.6 -male,165.5 -male,173.5 -male,157.1 -male,180.8 -male,168.3 -male,161.7 -male,181.5 -male,160.6 -male,165.6 -male,171.4 -male,183.6 -male,171.7 -male,180.3 -male,186.1 -male,170.5 -male,165.9 -male,165.9 -male,177.8 -male,164.6 -male,177.1 -male,169.6 -male,170.1 -male,174.3 -male,179.0 -male,180.9 -male,156.9 -male,164.9 -male,136.5 -male,182.2 -male,173.3 -male,170.6 -male,178.6 -male,170.6 -male,159.2 -male,174.1 -male,157.3 -male,170.1 -male,161.9 -male,188.1 -male,173.2 -male,167.6 -male,179.9 -male,162.4 -male,147.7 -male,170.2 -male,183.4 -male,178.3 -male,187.8 -male,161.5 -male,174.9 -male,158.6 -male,166.4 -male,181.5 -male,164.7 -male,174.9 -male,172.3 -male,176.0 -male,154.9 -male,165.2 -male,168.6 -male,176.6 -male,177.0 -male,179.0 -male,176.1 -male,164.2 -male,174.8 -male,158.7 -male,174.2 -male,186.1 -male,171.9 -male,172.3 -male,180.7 -male,171.1 -male,165.4 -male,165.1 -male,176.9 -male,165.9 -male,176.2 -male,172.9 -male,171.4 -male,171.4 -male,176.7 -male,174.4 -male,178.8 -male,174.2 -male,177.5 -male,178.0 -male,181.9 -male,174.5 -male,163.1 -male,166.3 -male,169.3 -male,165.9 -male,176.6 -male,176.7 -male,168.5 -male,192.9 -male,188.5 -male,172.1 -male,168.1 -male,178.7 -male,175.1 -male,166.2 -male,167.6 -male,162.6 -male,169.2 -male,159.5 -male,171.4 -male,167.7 -male,175.2 -male,173.8 -male,172.0 -male,171.8 -male,166.4 -male,168.7 -male,186.3 -male,181.8 -male,168.0 -male,170.0 -male,162.3 -male,183.3 -male,174.5 -male,173.7 -male,170.5 -male,165.9 -male,193.9 -male,173.9 -male,167.7 -male,169.0 -male,169.6 -male,178.7 -male,167.5 -male,168.5 -male,170.0 -male,171.0 -male,172.5 -male,165.2 -male,175.8 -male,166.0 -male,181.8 -male,183.5 -male,169.2 -male,166.8 -male,173.2 -male,160.1 -male,171.1 -male,189.1 -male,173.0 -male,165.0 -male,162.5 -male,187.9 -male,173.5 -male,168.5 -male,173.0 -male,180.0 -male,177.1 -male,178.2 -male,162.5 -male,173.1 -male,178.0 -male,161.8 -male,177.3 -male,156.9 -male,177.4 -male,174.5 -male,170.4 -male,170.4 -male,172.0 -male,166.3 -male,186.1 -male,175.3 -male,165.6 -male,166.8 -male,189.9 -male,169.3 -male,166.7 -male,176.1 -male,175.4 -male,168.3 -male,184.8 -male,175.9 -male,183.7 -male,174.6 -male,170.0 -male,166.7 -male,172.1 -male,177.0 -male,182.6 -male,183.3 -male,171.0 -male,159.1 -male,162.1 -male,161.6 -male,180.6 -male,153.7 -male,162.9 -male,168.3 -male,174.6 -male,178.2 -male,176.2 -male,179.9 -male,179.7 -male,167.2 -male,182.0 -male,171.8 -male,172.4 -male,179.3 -male,163.9 -male,159.6 -male,160.7 -male,169.6 -male,160.9 -male,166.6 -male,172.9 -male,162.5 -male,187.7 -male,178.7 -male,172.1 -male,174.9 -male,175.6 -male,171.4 -male,182.1 -male,164.7 -male,178.9 -male,157.9 -male,164.1 -male,176.6 -male,175.8 -male,170.9 -male,181.7 -male,173.9 -male,182.0 -male,166.4 -male,162.8 -male,173.4 -male,173.8 -male,157.2 -male,169.8 -male,168.0 -male,164.2 -male,178.5 -male,171.7 -male,180.5 -male,175.6 -male,157.5 -male,174.0 -male,175.8 -male,179.6 -male,177.9 -male,183.4 -male,185.4 -male,170.1 -male,183.6 -male,179.2 -male,168.2 -male,168.6 -male,160.6 -male,191.1 -male,167.6 -male,178.3 -male,175.2 -male,180.7 -male,164.2 -male,162.3 -male,180.6 -male,157.7 -male,160.7 -male,164.8 -male,170.6 -male,174.2 -male,164.1 -male,166.6 -male,168.1 -male,171.7 -male,168.1 -male,183.2 -male,178.0 -male,184.2 -male,175.8 -male,170.6 -male,183.4 -male,182.9 -male,162.2 -male,176.5 -male,174.3 -male,159.4 -male,173.4 -male,157.0 -male,177.8 -male,171.6 -male,176.4 -male,174.3 -male,165.5 -male,189.3 -male,169.9 -male,171.2 -male,173.9 -male,172.2 -male,168.9 -male,161.9 -male,175.3 -male,173.2 -male,181.9 -male,183.0 -male,166.3 -male,171.7 -male,169.2 -male,184.3 -male,167.4 -male,175.9 -male,190.1 -male,160.4 -male,173.4 -male,164.3 -male,187.4 -male,172.0 -male,176.7 -male,171.3 -male,168.4 -male,166.7 -male,167.4 -male,171.4 -male,165.4 -male,165.0 -male,164.0 -male,167.8 -male,176.4 -male,166.4 -male,176.4 -male,161.1 -male,184.1 -male,175.2 -male,168.0 -male,177.0 -male,165.1 -male,173.6 -male,168.7 -male,167.8 -male,185.1 -male,187.0 -male,178.5 -male,172.5 -male,171.9 -male,186.0 -male,182.2 -male,162.2 -male,171.5 -male,184.3 -male,181.3 -male,185.4 -male,164.4 -male,180.4 -male,180.7 -male,169.8 -male,171.8 -male,170.5 -male,178.0 -male,154.1 -male,185.5 -male,179.2 -male,181.3 -male,188.5 -male,171.7 -male,175.3 -male,174.0 -male,186.5 -male,161.3 -male,184.8 -male,195.0 -male,182.4 -male,168.4 -male,161.9 -male,165.8 -male,158.7 -male,175.9 -male,179.0 -male,194.5 -male,170.0 -male,175.9 -male,170.8 -male,185.8 -male,170.8 -male,162.1 -male,178.7 -male,177.1 -male,175.5 -male,178.3 -male,183.7 -male,185.1 -male,178.5 -male,173.9 -male,188.4 -male,181.8 -male,164.8 -male,187.4 -male,176.8 -male,184.1 -male,170.9 -male,182.3 -male,171.4 -male,177.9 -male,172.4 -male,164.7 -male,167.5 -male,172.9 -male,173.0 -male,157.1 -male,173.1 -male,164.3 -male,171.3 -male,167.5 -male,179.9 -male,177.7 -male,179.2 -male,171.8 -male,170.1 -male,171.7 -male,170.0 -male,176.6 -male,163.6 -male,178.0 -male,172.3 -male,175.2 -male,165.1 -male,169.3 -male,169.4 -male,170.5 -male,178.7 -male,172.8 -male,169.4 -male,178.7 -male,178.4 -male,165.8 -male,171.4 -male,170.8 -male,172.1 -male,172.0 -male,166.4 -male,175.8 -male,175.8 -male,180.4 -male,177.1 -male,177.2 -male,169.1 -male,191.3 -male,172.9 -male,173.2 -male,176.9 -male,177.5 -male,180.9 -male,180.1 -male,174.4 -male,168.4 -male,168.8 -male,173.1 -male,172.9 -male,168.3 -male,183.0 -male,176.5 -male,177.8 -male,179.8 -male,167.7 -male,178.0 -male,166.9 -male,167.7 -male,173.0 -male,160.2 -male,166.3 -male,166.2 -male,170.7 -male,179.5 -male,161.4 -male,169.4 -male,178.2 -male,172.7 -male,177.7 -male,166.8 -male,174.3 -male,170.5 -male,170.8 -male,176.2 -male,194.0 -male,151.7 -male,167.7 -male,169.0 -male,175.8 -male,179.4 -male,175.9 -male,166.2 -male,180.9 -male,168.4 -male,165.0 -male,187.9 -male,174.2 -male,173.6 -male,168.6 -male,168.5 -male,165.4 -male,166.9 -male,176.4 -male,170.8 -male,167.2 -male,172.6 -male,162.7 -male,174.3 -male,182.0 -male,181.9 -male,177.0 -male,165.5 -male,172.6 -male,184.1 -male,170.9 -male,171.3 -male,164.6 -male,166.6 -male,181.9 -male,174.6 -male,171.0 -male,165.7 -male,193.1 -male,175.5 -male,190.0 -male,170.1 -male,177.6 -male,166.9 -male,189.6 -male,166.5 -male,181.1 -male,155.0 -male,178.1 -male,172.1 -male,179.3 -male,178.1 -male,189.4 -male,182.8 -male,171.9 -male,171.3 -male,168.9 -male,176.1 -male,178.1 -male,168.7 -male,170.6 -male,185.3 -male,176.6 -male,175.4 -male,174.1 -male,186.0 -male,168.8 -male,168.1 -male,184.8 -male,170.0 -male,172.8 -male,177.2 -male,181.0 -male,167.1 -male,175.5 -male,163.7 -male,177.2 -male,159.0 -male,171.3 -male,169.4 -male,179.5 -male,177.2 -male,167.1 -male,164.6 -male,183.6 -male,167.2 -male,190.9 -male,188.4 -male,180.0 -male,176.3 -male,188.0 -male,175.7 -male,170.7 -male,183.5 -male,166.2 -male,185.4 -male,167.6 -male,168.9 -male,173.1 -male,164.7 -male,170.4 -male,173.6 -male,169.4 -male,159.1 -male,163.1 -male,185.5 -male,174.8 -male,158.9 -male,181.0 -male,177.1 -male,172.5 -male,173.0 -male,164.6 -male,184.1 -male,161.5 -male,185.1 -male,188.2 -male,180.9 -male,168.1 -male,176.1 -male,175.6 -male,162.1 -male,183.6 -male,169.8 -male,157.7 -male,171.7 -male,163.5 -male,182.6 -male,171.6 -male,172.9 -male,180.1 -male,160.5 -male,172.5 -male,170.9 -male,173.1 -male,180.0 -male,152.5 -male,172.6 -male,180.1 -male,176.2 -male,175.6 -male,175.8 -male,169.3 -male,171.9 -male,166.2 -male,167.8 -male,179.8 -male,174.0 -male,169.5 -male,171.7 -male,165.5 -male,185.7 -male,176.5 -male,157.6 -male,156.6 -male,177.9 -male,185.1 -male,165.8 -male,164.8 -male,185.5 -male,175.2 -male,164.4 -male,180.7 -male,173.2 -male,173.3 -male,170.0 -male,182.2 -male,169.8 -male,182.2 -male,174.4 -male,159.8 -male,172.6 -male,181.5 -male,169.7 -male,172.5 -male,179.1 -male,178.9 -male,186.9 -male,184.6 -male,174.5 -male,170.3 -male,176.9 -male,165.6 -male,171.1 -male,174.4 -male,161.9 -male,181.7 -male,171.9 -male,186.0 -male,178.8 -male,174.1 -male,173.9 -male,159.0 -male,165.2 -male,186.5 -male,165.2 -male,183.2 -male,178.9 -male,173.4 -male,173.0 -male,160.7 -male,165.1 -male,176.9 -male,166.7 -male,174.4 -male,153.3 -male,169.0 -male,167.4 -male,172.7 -male,156.1 -male,189.3 -male,179.4 -male,172.9 -male,168.0 -male,173.1 -male,174.3 -male,171.4 -male,171.9 -male,180.0 -male,179.6 -male,175.3 -male,158.4 -male,168.3 -male,167.7 -male,163.4 -male,172.3 -male,170.6 -male,185.2 -male,161.9 -male,172.6 -male,162.9 -male,161.8 -male,157.4 -male,169.9 -male,184.2 -male,174.5 -male,172.3 -male,161.9 -male,172.0 -male,178.7 -male,170.7 -male,179.1 -male,178.4 -male,167.0 -male,164.6 -male,176.0 -male,192.3 -male,161.7 -male,174.3 -male,178.3 -male,174.8 -male,169.5 -male,172.3 -male,179.5 -male,184.9 -male,171.9 -male,175.3 -male,170.9 -male,176.2 -male,169.3 -male,172.6 -male,166.7 -male,162.6 -male,180.0 -male,159.3 -male,173.8 -male,180.0 -male,173.8 -male,182.1 -male,179.4 -male,165.1 -male,171.0 -male,172.2 -male,195.5 -male,169.9 -male,165.2 -male,154.0 -male,176.0 -male,170.0 -male,168.4 -male,168.7 -male,183.6 -male,179.0 -male,178.9 -male,170.4 -male,178.1 -male,171.6 -male,159.7 -male,187.7 -male,171.0 -male,173.4 -male,172.6 -male,174.6 -male,183.4 -male,180.9 -male,177.6 -male,170.6 -male,176.0 -male,169.0 -male,175.5 -male,185.8 -male,177.7 -male,184.7 -male,190.2 -male,166.2 -male,171.9 -male,168.6 -male,179.8 -male,176.4 -male,178.7 -male,155.8 -male,172.3 -male,179.2 -male,174.4 -male,167.8 -male,159.5 -male,185.7 -male,181.6 -male,164.4 -male,176.9 -male,166.0 -male,197.7 -male,161.1 -male,180.3 -male,176.6 -male,161.0 -male,185.9 -male,174.9 -male,174.9 -male,164.5 -male,173.2 -male,163.9 -male,171.1 -male,185.2 -male,177.4 -male,174.7 -male,180.9 -male,167.3 -male,172.1 -male,172.2 -male,165.8 -male,160.8 -male,176.6 -male,171.1 -male,177.2 -male,192.5 -male,184.8 -male,182.8 -male,167.5 -male,173.3 -male,184.9 -male,183.7 -male,168.8 -male,166.3 -male,170.1 -male,169.1 -male,178.0 -male,174.4 -male,171.1 -male,172.6 -male,175.8 -male,157.5 -male,170.4 -male,177.4 -male,180.3 -male,170.2 -male,167.7 -male,168.4 -male,179.3 -male,184.8 -male,172.4 -male,175.8 -male,166.8 -male,165.9 -male,167.3 -male,169.0 -male,166.9 -male,179.5 -male,171.0 -male,175.6 -male,177.5 -male,171.8 -male,161.3 -male,175.3 -male,159.9 -male,190.5 -male,159.6 -male,163.0 -male,165.9 -male,181.9 -male,173.4 -male,169.0 -male,166.3 -male,157.6 -male,181.8 -male,175.0 -male,167.7 -male,165.2 -male,173.0 -male,180.4 -male,179.0 -male,174.1 -male,181.0 -male,180.5 -male,173.6 -male,172.4 -male,166.4 -male,166.0 -male,174.2 -male,159.9 -male,167.6 -male,172.9 -male,169.8 -male,180.7 -male,168.1 -male,174.4 -male,176.2 -male,185.2 -male,167.1 -male,176.4 -male,178.9 -male,178.3 -male,161.8 -male,185.0 -male,184.0 -male,160.1 -male,175.1 -male,186.2 -male,180.4 -male,174.2 -male,171.5 -male,174.6 -male,176.2 -male,157.5 -male,178.2 -male,178.1 -male,183.0 -male,187.0 -male,178.7 -male,176.8 -male,172.2 -male,181.2 -male,171.1 -male,173.6 -male,173.3 -male,176.7 -male,169.2 -male,183.2 -male,165.7 -male,179.9 -male,172.5 -male,168.5 -male,179.4 -male,168.2 -male,175.9 -male,179.2 -male,170.7 -male,176.2 -male,169.3 -male,179.6 -male,162.0 -male,169.8 -male,170.3 -male,172.3 -male,191.8 -male,191.9 -male,177.9 -male,178.3 -male,170.4 -male,185.6 -male,176.4 -male,159.0 -male,173.2 -male,167.8 -male,165.1 -male,159.6 -male,176.8 -male,160.3 -male,169.7 -male,173.2 -male,174.0 -male,164.5 -male,164.9 -male,172.2 -male,180.5 -male,166.4 -male,175.5 -male,161.5 -male,182.6 -male,177.6 -male,181.5 -male,181.6 -male,167.9 -male,162.6 -male,165.6 -male,164.5 -male,184.4 -male,158.8 -male,168.7 -male,169.6 -male,182.3 -male,177.6 -male,166.2 -male,189.1 -male,176.9 -male,164.4 -male,180.5 -male,175.1 -male,184.8 -male,170.2 -male,171.3 -male,165.1 -male,186.8 -male,168.1 -male,184.4 -male,167.7 -male,169.5 -male,182.7 -male,183.9 -male,164.9 -male,182.2 -male,168.0 -male,172.8 -male,182.0 -male,167.3 -male,166.3 -male,173.4 -male,171.9 -male,180.6 -male,176.2 -male,155.5 -male,178.0 -male,167.2 -male,164.3 -male,159.1 -male,182.1 -male,177.7 -male,181.3 -male,162.9 -male,179.0 -male,175.0 -male,183.4 -male,182.4 -male,176.7 -male,170.4 -male,181.7 -male,182.3 -male,157.5 -male,171.2 -male,173.9 -male,177.6 -male,179.1 -male,189.0 -male,171.6 -male,170.9 -male,173.2 -male,161.4 -male,180.2 -male,151.9 -male,171.3 -male,166.0 -male,167.9 -male,183.1 -male,174.3 -male,176.1 -male,172.0 -male,163.2 -male,173.2 -male,178.1 -male,164.1 -male,177.2 -male,169.7 -male,177.8 -male,165.0 -male,174.4 -male,164.6 -male,170.7 -male,165.3 -male,172.1 -male,187.9 -male,183.9 -male,169.5 -male,177.4 -male,166.9 -male,174.4 -male,177.8 -male,167.6 -male,185.5 -male,182.1 -male,181.7 -male,172.5 -male,154.6 -male,166.4 -male,167.5 -male,170.2 -male,162.0 -male,171.6 -male,173.1 -male,175.8 -male,162.6 -male,178.3 -male,160.3 -male,166.2 -male,172.4 -male,174.5 -male,173.6 -male,165.8 -male,181.4 -male,166.5 -male,178.6 -male,164.3 -male,167.7 -male,175.1 -male,183.2 -male,175.0 -male,170.1 -male,166.0 -male,171.4 -male,160.0 -male,183.0 -male,179.3 -male,178.2 -male,153.8 -male,170.9 -male,172.4 -male,181.8 -male,169.2 -male,178.4 -male,160.6 -male,182.7 -male,176.4 -male,176.8 -male,165.2 -male,180.1 -male,175.0 -male,173.0 -male,176.4 -male,167.8 -male,182.8 -male,175.8 -male,180.6 -male,168.0 -male,157.8 -male,167.1 -male,175.3 -male,168.4 -male,174.7 -male,166.3 -male,175.4 -male,179.1 -male,172.2 -male,166.9 -male,176.5 -male,181.2 -male,176.0 -male,178.1 -male,171.7 -male,176.5 -male,168.4 -male,167.0 -male,174.0 -male,188.0 -male,161.1 -male,163.1 -male,166.9 -male,174.7 -male,160.8 -male,167.9 -male,168.3 -male,166.5 -male,192.9 -male,184.9 -male,159.1 -male,171.6 -male,168.9 -male,164.9 -male,168.9 -male,175.0 -male,190.8 -male,179.5 -male,176.4 -male,177.1 -male,177.0 -male,166.8 -male,182.0 -male,166.6 -male,173.9 -male,173.2 -male,195.5 -male,171.8 -male,188.4 -male,160.6 -male,158.5 -male,169.3 -male,174.6 -male,175.0 -male,176.6 -male,158.3 -male,168.5 -male,179.3 -male,170.1 -male,186.5 -male,187.5 -male,171.9 -male,171.1 -male,162.1 -male,175.7 -male,174.3 -male,165.1 -male,169.7 -male,173.4 -male,172.6 -male,166.6 -male,177.5 -male,168.8 -male,169.4 -male,179.3 -male,168.2 -male,180.6 -male,181.0 -male,173.8 -male,176.1 -male,167.0 -male,174.2 -male,169.1 -male,183.5 -male,174.5 -male,171.7 -male,169.6 -male,167.8 -male,177.9 -male,166.5 -male,171.5 -male,165.4 -male,181.7 -male,174.8 -male,182.0 -male,178.6 -male,167.8 -male,163.2 -male,180.5 -male,167.3 -male,165.9 -male,172.8 -male,175.5 -male,185.4 -male,172.6 -male,169.1 -male,175.5 -male,179.6 -male,180.5 -male,183.3 -male,177.9 -male,176.1 -male,158.8 -male,177.6 -male,174.0 -male,170.8 -male,185.8 -male,175.1 -male,175.5 -male,175.5 -male,163.5 -male,164.1 -male,179.0 -male,162.5 -male,178.5 -male,182.2 -male,171.3 -male,170.4 -male,175.0 -male,173.5 -male,159.9 -male,179.3 -male,173.7 -male,170.3 -male,167.5 -male,167.3 -male,169.4 -male,172.6 -male,186.1 -male,175.9 -male,154.4 -male,181.6 -male,177.2 -male,173.9 -male,161.2 -male,181.4 -male,165.7 -male,171.0 -male,183.1 -male,171.3 -male,166.8 -male,163.3 -male,171.9 -male,182.9 -male,188.1 -male,183.3 -male,170.5 -male,170.9 -male,182.7 -male,178.9 -male,181.5 -male,178.4 -male,168.9 -male,169.3 -male,185.0 -male,189.5 -male,168.8 -male,185.9 -male,176.6 -male,177.0 -male,167.5 -male,171.6 -male,165.7 -male,175.3 -male,169.1 -male,166.9 -male,170.1 -male,166.6 -male,163.8 -male,175.0 -male,185.2 -male,169.5 -male,172.8 -male,163.8 -male,169.1 -male,168.4 -male,169.7 -male,179.2 -male,169.0 -male,174.0 -male,176.2 -male,163.1 -male,168.8 -male,178.4 -male,180.1 -male,170.5 -male,175.8 -male,174.7 -male,172.7 -male,158.5 -male,171.2 -male,176.4 -male,169.6 -male,177.9 -male,184.2 -male,161.5 -male,185.6 -male,182.4 -male,170.0 -male,177.3 -male,174.5 -male,171.3 -male,169.6 -male,179.2 -male,171.8 -male,174.8 -male,175.7 -male,170.5 -male,159.7 -male,181.8 -male,170.7 -male,166.4 -male,180.1 -male,174.7 -male,170.9 -male,176.1 -male,173.6 -male,179.4 -male,176.0 -male,167.4 -male,167.4 -male,169.8 -male,171.4 -male,164.2 -male,155.4 -male,180.8 -male,180.4 -male,168.6 -male,168.4 -male,178.4 -male,178.8 -male,168.2 -male,165.0 -male,167.9 -male,170.2 -male,170.3 -male,168.9 -male,170.5 -male,177.3 -male,177.2 -male,164.2 -male,175.0 -male,188.6 -male,167.6 -male,168.5 -male,173.1 -male,172.5 -male,156.9 -male,171.0 -male,187.3 -male,177.0 -male,189.1 -male,162.3 -male,164.9 -male,175.3 -male,170.9 -male,162.7 -male,177.1 -male,171.4 -male,172.8 -male,167.6 -male,178.4 -male,179.0 -male,170.9 -male,171.4 -male,178.1 -male,165.2 -male,155.3 -male,161.3 -male,187.2 -male,177.7 -male,168.8 -male,180.2 -male,182.5 -male,164.6 -male,175.2 -male,172.4 -male,180.8 -male,160.4 -male,178.7 -male,164.3 -male,169.4 -male,162.5 -male,178.6 -male,180.1 -male,177.5 -male,169.3 -male,168.5 -male,181.3 -male,175.9 -male,184.9 -male,168.4 -male,158.8 -male,174.8 -male,172.8 -male,173.5 -male,173.6 -male,175.9 -male,171.2 -male,163.3 -male,174.6 -male,177.5 -male,166.9 -male,167.9 -male,165.9 -male,166.7 -male,179.5 -male,174.1 -male,169.9 -male,178.7 -male,171.3 -male,164.1 -male,169.6 -male,176.7 -male,177.5 -male,154.8 -male,183.5 -male,176.0 -male,172.2 -male,175.7 -male,172.3 -male,172.6 -male,171.9 -male,177.2 -male,174.4 -male,179.4 -male,156.9 -male,176.4 -male,166.7 -male,187.0 -male,181.7 -male,177.8 -male,153.1 -male,166.2 -male,158.4 -male,171.7 -male,177.7 -male,178.6 -male,189.7 -male,164.3 -male,181.9 -male,165.8 -male,169.2 -male,163.1 -male,164.6 -male,180.5 -male,180.7 -male,182.0 -male,162.8 -male,174.2 -male,173.0 -male,185.0 -male,171.8 -male,166.1 -male,168.1 -male,164.8 -male,175.0 -male,173.4 -male,175.1 -male,180.0 -male,179.1 -male,163.8 -male,168.8 -male,174.3 -male,172.3 -male,184.7 -male,187.8 -male,174.0 -male,177.4 -male,175.0 -male,160.8 -male,165.6 -male,175.5 -male,149.8 -male,172.6 -male,166.0 -male,174.8 -male,180.8 -male,167.8 -male,157.0 -male,179.6 -male,176.3 -male,166.1 -male,165.8 -male,173.6 -male,175.6 -male,175.1 -male,182.1 -male,157.1 -male,181.7 -male,172.3 -male,163.5 -male,178.3 -male,162.0 -male,176.3 -male,181.6 -male,169.7 -male,167.3 -male,176.3 -male,179.5 -male,175.5 -male,164.9 -male,174.9 -male,160.7 -male,176.3 -male,173.5 -male,171.8 -male,160.1 -male,174.8 -male,167.4 -male,175.0 -male,171.7 -male,189.1 -male,176.4 -male,155.9 -male,167.9 -male,169.2 -male,182.0 -male,172.1 -male,171.3 -male,160.1 -male,173.7 -male,163.6 -male,164.9 -male,168.4 -male,168.0 -male,173.5 -male,171.6 -male,186.0 -male,172.7 -male,174.2 -male,177.5 -male,171.5 -male,174.4 -male,176.8 -male,159.8 -male,178.8 -male,174.4 -male,180.6 -male,167.2 -male,171.4 -male,194.6 -male,171.0 -male,171.0 -male,185.4 -male,161.7 -male,172.5 -male,161.4 -male,169.9 -male,173.0 -male,177.9 -male,163.7 -male,157.8 -male,169.8 -male,168.3 -male,182.0 -male,175.5 -male,167.3 -male,175.9 -male,170.4 -male,181.0 -male,176.1 -male,166.6 -male,173.8 -male,179.4 -male,183.0 -male,172.5 -male,158.9 -male,163.9 -male,172.9 -male,169.0 -male,173.9 -male,179.4 -male,191.7 -male,182.5 -male,180.8 -male,166.0 -male,168.4 -male,163.7 -male,164.0 -male,168.5 -male,174.2 -male,168.2 -male,152.8 -male,176.9 -male,167.1 -male,170.9 -male,169.7 -male,181.2 -male,191.0 -male,162.1 -male,179.8 -male,173.4 -male,163.9 -male,173.6 -male,170.5 -male,178.2 -male,172.7 -male,174.6 -male,185.7 -male,167.3 -male,168.9 -male,181.9 -male,184.3 -male,178.4 -male,167.0 -male,167.4 -male,170.6 -male,161.6 -male,179.1 -male,182.9 -male,166.0 -male,179.4 -male,177.3 -male,159.9 -male,162.7 -male,184.5 -male,176.5 -male,180.2 -male,168.1 -male,181.2 -male,178.5 -male,187.2 -male,165.0 -male,160.6 -male,172.2 -male,179.2 -male,174.2 -male,167.6 -male,172.9 -male,174.4 -male,178.3 -male,188.6 -male,180.9 -male,176.3 -male,159.3 -male,183.7 -male,179.8 -male,162.8 -male,176.7 -male,175.5 -male,175.8 -male,164.7 -male,171.0 -male,173.3 -male,164.7 -male,167.2 -male,166.1 -male,181.4 -male,167.7 -male,180.9 -male,190.1 -male,175.6 -male,165.0 -male,181.6 -male,178.2 -male,168.1 -male,177.2 -male,176.9 -male,181.6 -male,168.2 -male,173.3 -male,175.7 -male,154.2 -male,183.3 -male,171.4 -male,161.6 -male,167.2 -male,178.9 -male,155.4 -male,177.6 -male,176.0 -male,167.3 -male,166.9 -male,182.4 -male,179.2 -male,166.9 -male,174.3 -male,174.7 -male,161.4 -male,161.1 -male,180.9 -male,169.4 -male,174.2 -male,159.2 -male,162.8 -male,163.4 -male,187.2 -male,174.7 -male,173.2 -male,174.2 -male,175.3 -male,177.0 -male,176.8 -male,182.0 -male,173.0 -male,152.1 -male,168.7 -male,187.8 -male,168.8 -male,179.6 -male,175.8 -male,176.3 -male,159.6 -male,171.9 -male,178.4 -male,161.4 -male,172.1 -male,163.6 -male,180.4 -male,176.4 -male,170.5 -male,170.2 -male,171.8 -male,167.4 -male,178.0 -male,172.8 -male,177.0 -male,171.1 -male,171.7 -male,181.0 -male,181.6 -male,176.4 -male,177.3 -male,173.2 -male,178.1 -male,189.5 -male,174.2 -male,169.1 -male,179.4 -male,168.4 -male,189.9 -male,181.9 -male,179.1 -male,185.8 -male,171.3 -male,176.2 -male,170.0 -male,176.2 -male,175.6 -male,169.2 -male,163.8 -male,164.0 -male,182.1 -male,166.0 -male,169.3 -male,178.1 -male,164.4 -male,187.1 -male,179.6 -male,173.3 -male,166.8 -male,169.7 -male,171.1 -male,167.6 -male,166.3 -male,180.6 -male,180.2 -male,187.6 -male,184.8 -male,178.3 -male,164.6 -male,191.5 -male,171.9 -male,184.6 -male,178.6 -male,177.6 -male,181.3 -male,167.4 -male,181.1 -male,153.9 -male,165.6 -male,190.3 -male,173.5 -male,174.8 -male,168.5 -male,167.0 -male,177.1 -male,166.0 -male,178.3 -male,185.4 -male,175.4 -male,189.2 -male,176.5 -male,175.4 -male,175.0 -male,170.3 -male,176.2 -male,166.5 -male,177.9 -male,175.5 -male,171.1 -male,169.5 -male,161.7 -male,173.3 -male,176.8 -male,175.0 -male,170.6 -male,176.4 -male,176.6 -male,164.6 -male,166.8 -male,178.0 -male,160.9 -male,173.4 -male,170.9 -male,173.8 -male,174.4 -male,179.9 -male,166.0 -male,179.1 -male,172.7 -male,180.5 -male,181.5 -male,173.9 -male,173.5 -male,169.0 -male,164.9 -male,173.7 -male,172.5 -male,181.6 -male,164.5 -male,188.2 -male,175.0 -male,180.6 -male,170.1 -male,156.8 -male,181.2 -male,169.1 -male,183.1 -male,177.2 -male,157.7 -male,179.6 -male,166.5 -male,173.8 -male,188.7 -male,183.7 -male,177.7 -male,161.4 -male,178.7 -male,181.1 -male,175.2 -male,171.9 -male,165.5 -male,171.1 -male,171.8 -male,172.7 -male,180.0 -male,164.7 -male,164.0 -male,160.7 -male,169.4 -male,164.8 -male,177.2 -male,166.0 -male,170.2 -male,171.3 -male,168.1 -male,166.8 -male,177.0 -male,188.1 -male,185.6 -male,181.8 -male,184.6 -male,170.0 -male,173.9 -male,164.2 -male,179.3 -male,166.7 -male,177.4 -male,174.1 -male,192.8 -male,176.7 -male,175.7 -male,155.5 -male,172.3 -male,175.5 -male,169.4 -male,164.8 -male,158.9 -male,170.4 -male,171.9 -male,176.6 -male,173.1 -male,168.7 -male,187.2 -male,184.4 -male,185.0 -male,177.6 -male,170.0 -male,176.4 -male,178.0 -male,182.4 -male,183.8 -male,165.9 -male,172.0 -male,174.5 -male,189.6 -male,171.9 -male,180.3 -male,166.9 -male,166.4 -male,182.1 -male,178.4 -male,170.0 -male,173.7 -male,178.4 -male,173.1 -male,163.6 -male,178.0 -male,168.7 -male,169.6 -male,175.5 -male,164.5 -male,194.6 -male,186.3 -male,186.3 -male,170.1 -male,172.8 -male,181.0 -male,164.9 -male,166.7 -male,163.8 -male,170.3 -male,178.9 -male,185.3 -male,185.3 -male,168.0 -male,182.9 -male,176.2 -male,182.3 -male,184.1 -male,169.2 -male,164.1 -male,161.1 -male,155.8 -male,173.1 -male,184.9 -male,181.9 -male,173.1 -male,168.5 -male,183.4 -male,173.5 -male,167.7 -male,180.4 -male,178.2 -male,186.0 -male,168.4 -male,178.7 -male,162.5 -male,166.4 -male,176.0 -male,162.8 -male,184.3 -male,178.4 -male,170.2 -male,177.3 -male,182.7 -male,165.8 -male,176.7 -male,169.6 -male,167.0 -male,184.7 -male,172.5 -male,171.3 -male,175.1 -male,172.6 -male,169.6 -male,189.3 -male,166.7 -male,165.1 -male,185.3 -male,177.1 -male,172.8 -male,167.4 -male,170.6 -male,174.1 -male,164.6 -male,165.3 -male,184.2 -male,180.8 -male,185.5 -male,179.6 -male,177.7 -male,175.6 -male,189.6 -male,184.0 -male,185.5 -male,176.3 -male,182.3 -male,185.6 -male,172.0 -male,182.2 -male,178.2 -male,163.1 -male,169.5 -male,188.3 -male,164.5 -male,183.8 -male,172.3 -male,165.0 -male,173.1 -male,171.5 -male,161.2 -male,168.1 -male,169.7 -male,175.7 -male,168.6 -male,182.3 -male,167.0 -male,179.2 -male,164.9 -male,167.8 -male,168.5 -male,178.6 -male,167.9 -male,167.7 -male,188.2 -male,178.6 -male,177.1 -male,174.2 -male,171.1 -male,174.1 -male,175.5 -male,166.8 -male,189.0 -male,175.3 -male,168.7 -male,175.7 -male,180.0 -male,170.9 -male,169.7 -male,166.5 -male,182.8 -male,178.8 -male,181.1 -male,180.3 -male,180.6 -male,175.3 -male,182.4 -male,163.8 -male,177.6 -male,170.9 -male,163.8 -male,176.7 -male,171.4 -male,169.2 -male,182.0 -male,171.5 -male,179.5 -male,166.6 -male,168.2 -male,176.6 -male,164.1 -male,181.4 -male,171.3 -male,185.1 -male,175.7 -male,181.7 -male,169.2 -male,168.9 -male,187.0 -male,181.2 -male,172.0 -male,171.5 -male,177.0 -male,170.5 -male,177.7 -male,169.9 -male,184.8 -male,165.4 -male,170.2 -male,176.3 -male,159.8 -male,179.0 -male,158.3 -male,169.3 -male,187.6 -male,172.2 -male,173.9 -male,180.7 -male,175.0 -male,175.2 -male,175.0 -male,179.2 -male,172.9 -male,171.7 -male,172.9 -male,178.2 -male,167.0 -male,177.8 -male,182.6 -male,180.9 -male,175.4 -male,170.5 -male,157.9 -male,167.7 -male,187.6 -male,180.9 -male,178.9 -male,175.5 -male,173.2 -male,163.3 -male,166.8 -male,190.8 -male,189.9 -male,170.2 -male,173.9 -male,176.8 -male,162.0 -male,169.3 -male,173.5 -male,186.4 -male,165.9 -male,169.6 -male,175.5 -male,176.4 -male,164.9 -male,168.5 -male,166.9 -male,167.3 -male,174.7 -male,171.2 -male,177.4 -male,174.9 -male,182.1 -male,176.4 -male,174.4 -male,164.9 -male,178.8 -male,176.7 -male,168.2 -male,180.0 -male,177.7 -male,173.7 -male,161.2 -male,156.9 -male,177.8 -male,171.6 -male,183.3 -male,165.6 -male,162.8 -male,190.6 -male,172.3 -male,185.2 -male,178.8 -male,187.3 -male,172.2 -male,174.9 -male,181.8 -male,181.4 -male,170.5 -male,183.7 -male,160.3 -male,175.5 -male,172.3 -male,172.9 -male,175.4 -male,188.5 -male,157.7 -male,167.8 -male,171.6 -male,179.6 -male,173.9 -male,184.4 -male,168.7 -male,182.9 -male,183.1 -male,180.5 -male,177.0 -male,175.4 -male,169.3 -male,188.3 -male,168.9 -male,181.9 -male,171.7 -male,167.4 -male,169.1 -male,170.3 -male,179.1 -male,177.8 -male,182.9 -male,152.9 -male,170.1 -male,169.5 -male,166.7 -male,174.6 -male,177.7 -male,167.9 -male,161.8 -male,163.6 -male,171.9 -male,179.9 -male,184.2 -male,175.8 -male,178.3 -male,154.4 -male,164.3 -male,175.9 -male,172.5 -male,166.5 -male,166.7 -male,173.0 -male,173.7 -male,163.6 -male,193.3 -male,174.7 -male,186.2 -male,169.9 -male,177.0 -male,161.5 -male,168.7 -male,179.6 -male,175.5 -male,185.8 -male,180.0 -male,173.8 -male,164.9 -male,175.7 -male,176.4 -male,188.6 -male,180.7 -male,179.6 -male,175.1 -male,175.8 -male,173.5 -male,176.0 -male,190.2 -male,192.2 -male,165.1 -male,172.0 -male,178.7 -male,165.0 -male,171.9 -male,169.7 -male,176.9 -male,175.4 -male,178.4 -male,183.6 -male,167.7 -male,163.9 -male,175.6 -male,172.5 -male,170.8 -male,172.9 -male,179.8 -male,166.8 -male,169.3 -male,161.1 -male,179.1 -male,174.1 -male,182.2 -male,181.7 -male,171.7 -male,179.3 -male,175.4 -male,165.0 -male,178.3 -male,180.0 -male,172.4 -male,192.5 -male,181.9 -male,182.4 -male,174.7 -male,156.4 -male,192.5 -male,185.1 -male,169.1 -male,177.4 -male,180.4 -male,171.2 -male,178.4 -male,167.4 -male,166.1 -male,191.1 -male,166.8 -male,177.8 -male,177.0 -male,186.7 -male,181.2 -male,169.9 -male,184.3 -male,174.0 -male,184.4 -male,172.9 -male,176.9 -male,170.1 -male,165.8 -male,170.1 -male,185.4 -male,177.4 -male,189.0 -male,170.5 -male,172.2 -male,167.8 -male,171.6 -male,179.9 -male,174.7 -male,169.0 -male,195.6 -male,173.3 -male,170.3 -male,168.5 -male,180.2 -male,172.8 -male,166.8 -male,167.8 -male,177.1 -male,179.3 -male,164.4 -male,178.4 -male,178.5 -male,165.1 -male,174.0 -male,184.6 -male,169.9 -male,175.6 -male,173.4 -male,180.3 -male,186.6 -male,173.2 -male,185.5 -male,175.7 -male,169.9 -male,188.8 -male,180.8 -male,176.4 -male,173.7 -male,164.7 -male,182.5 -male,177.6 -male,171.4 -male,182.4 -male,181.5 -male,172.1 -male,172.8 -male,172.9 -male,162.0 -male,195.8 -male,185.0 -male,182.4 -male,157.7 -male,173.6 -male,170.0 -male,165.3 -male,163.7 -male,178.4 -male,182.7 -male,170.1 -male,175.5 -male,168.3 -male,166.2 -male,173.4 -male,173.9 -male,148.2 -male,175.6 -male,174.6 -male,183.7 -male,166.5 -male,171.4 -male,170.0 -male,172.4 -male,163.1 -male,172.2 -male,181.4 -male,185.3 -male,172.6 -male,161.7 -male,171.3 -male,178.9 -male,162.0 -male,170.3 -male,179.8 -male,172.2 -male,167.4 -male,177.1 -male,173.3 -male,168.2 -male,163.0 -male,169.1 -male,178.4 -male,164.9 -male,177.2 -male,189.3 -male,168.3 -male,174.7 -male,178.4 -male,169.6 -male,177.2 -male,175.0 -male,181.0 -male,175.6 -male,177.9 -male,175.6 -male,174.6 -male,174.9 -male,167.4 -male,186.3 -male,170.3 -male,168.1 -male,170.1 -male,175.1 -male,180.7 -male,163.6 -male,180.1 -male,173.9 -male,170.5 -male,182.6 -male,182.9 -male,168.1 -male,180.8 -male,172.5 -male,176.1 -male,178.1 -male,178.2 -male,174.5 -male,179.4 -male,174.6 -male,159.4 -male,181.8 -male,167.4 -male,178.4 -male,165.0 -male,164.0 -male,189.1 -male,184.2 -male,169.8 -male,179.1 -male,167.2 -male,174.1 -male,176.8 -male,170.9 -male,165.3 -male,191.5 -male,182.8 -male,178.4 -male,176.2 -male,176.3 -male,171.9 -male,168.8 -male,182.9 -male,171.0 -male,173.3 -male,184.3 -male,175.7 -male,177.9 -male,181.5 -male,172.0 -male,174.8 -male,180.0 -male,182.2 -male,165.0 -male,172.9 -male,164.8 -male,173.9 -male,168.8 -male,181.1 -male,165.1 -male,179.8 -male,167.8 -male,170.9 -male,185.0 -male,168.2 -male,183.1 -male,166.0 -male,164.6 -male,169.7 -male,155.1 -male,168.9 -male,163.8 -male,180.3 -male,174.0 -male,170.2 -male,170.6 -male,171.5 -male,169.6 -male,171.5 -male,169.0 -male,177.8 -male,175.5 -male,167.1 -male,181.8 -male,172.4 -male,172.4 -male,178.2 -male,156.5 -male,169.3 -male,170.9 -male,174.5 -male,183.0 -male,178.5 -male,163.1 -male,162.8 -male,170.4 -male,180.1 -male,164.9 -male,175.8 -female,160.9 -female,150.0 -female,151.3 -female,163.6 -female,164.1 -female,150.8 -female,156.4 -female,168.5 -female,149.9 -female,149.8 -female,160.2 -female,157.5 -female,160.7 -female,145.2 -female,152.0 -female,164.6 -female,167.6 -female,161.6 -female,157.1 -female,169.8 -female,166.8 -female,147.9 -female,159.2 -female,164.8 -female,150.0 -female,162.0 -female,157.7 -female,148.3 -female,171.5 -female,155.3 -female,166.7 -female,162.7 -female,159.0 -female,156.3 -female,160.2 -female,139.9 -female,163.1 -female,152.7 -female,143.9 -female,162.7 -female,152.4 -female,149.3 -female,149.3 -female,167.9 -female,154.5 -female,160.6 -female,165.9 -female,161.1 -female,159.1 -female,172.3 -female,156.0 -female,162.4 -female,154.1 -female,154.0 -female,156.3 -female,164.6 -female,170.2 -female,154.4 -female,152.3 -female,160.0 -female,153.8 -female,160.6 -female,162.9 -female,154.7 -female,166.5 -female,167.9 -female,149.4 -female,164.9 -female,167.5 -female,155.3 -female,152.1 -female,159.3 -female,151.4 -female,156.4 -female,176.2 -female,166.0 -female,157.3 -female,168.5 -female,159.8 -female,153.9 -female,160.8 -female,169.0 -female,162.5 -female,164.1 -female,161.3 -female,158.5 -female,163.4 -female,150.8 -female,161.2 -female,161.1 -female,165.0 -female,151.6 -female,157.1 -female,171.9 -female,154.3 -female,165.4 -female,158.0 -female,154.1 -female,161.4 -female,168.2 -female,158.5 -female,146.1 -female,157.4 -female,158.4 -female,161.0 -female,167.7 -female,162.7 -female,148.7 -female,159.4 -female,160.0 -female,149.6 -female,150.1 -female,155.9 -female,163.7 -female,174.5 -female,161.6 -female,153.7 -female,166.2 -female,159.3 -female,163.8 -female,144.2 -female,166.8 -female,157.2 -female,156.5 -female,153.8 -female,141.1 -female,160.2 -female,157.9 -female,157.6 -female,149.4 -female,170.0 -female,151.1 -female,157.4 -female,160.6 -female,162.2 -female,159.6 -female,156.8 -female,158.6 -female,166.6 -female,167.8 -female,162.1 -female,154.3 -female,165.9 -female,159.8 -female,163.5 -female,167.2 -female,165.3 -female,165.4 -female,162.6 -female,155.0 -female,142.9 -female,153.8 -female,158.1 -female,154.7 -female,153.2 -female,177.4 -female,164.3 -female,160.1 -female,168.9 -female,161.6 -female,158.3 -female,153.7 -female,151.8 -female,163.5 -female,160.8 -female,162.9 -female,152.9 -female,160.3 -female,166.3 -female,159.4 -female,155.5 -female,161.7 -female,154.2 -female,158.8 -female,160.8 -female,159.3 -female,166.3 -female,154.7 -female,152.3 -female,170.6 -female,152.3 -female,150.0 -female,158.0 -female,157.8 -female,166.7 -female,163.9 -female,153.8 -female,162.7 -female,168.8 -female,156.5 -female,171.0 -female,160.9 -female,156.5 -female,159.0 -female,150.8 -female,158.9 -female,148.4 -female,155.1 -female,155.4 -female,152.0 -female,157.4 -female,168.4 -female,155.7 -female,166.0 -female,171.0 -female,151.8 -female,164.9 -female,165.6 -female,162.1 -female,164.0 -female,154.5 -female,167.8 -female,154.2 -female,156.2 -female,156.6 -female,156.4 -female,154.3 -female,150.5 -female,161.5 -female,169.5 -female,163.4 -female,158.7 -female,153.4 -female,168.0 -female,169.4 -female,153.8 -female,158.9 -female,154.5 -female,156.1 -female,152.1 -female,163.0 -female,167.1 -female,160.9 -female,162.8 -female,155.8 -female,158.4 -female,156.6 -female,150.0 -female,161.0 -female,150.9 -female,158.6 -female,170.5 -female,153.6 -female,155.4 -female,155.1 -female,158.2 -female,145.0 -female,162.7 -female,153.1 -female,156.3 -female,152.0 -female,165.8 -female,164.0 -female,153.6 -female,168.9 -female,160.1 -female,158.4 -female,168.1 -female,163.9 -female,155.4 -female,161.5 -female,157.7 -female,158.7 -female,166.9 -female,164.8 -female,142.3 -female,166.6 -female,159.7 -female,151.9 -female,166.8 -female,158.7 -female,171.1 -female,171.7 -female,160.5 -female,161.8 -female,153.9 -female,167.6 -female,165.1 -female,162.4 -female,152.6 -female,156.9 -female,172.1 -female,157.6 -female,155.6 -female,162.4 -female,154.3 -female,165.7 -female,146.1 -female,170.4 -female,173.4 -female,141.9 -female,178.8 -female,162.1 -female,163.1 -female,155.0 -female,161.5 -female,166.8 -female,165.4 -female,157.8 -female,162.4 -female,159.8 -female,153.0 -female,161.9 -female,170.2 -female,155.7 -female,155.3 -female,163.9 -female,159.5 -female,169.2 -female,153.9 -female,163.7 -female,165.9 -female,163.2 -female,167.8 -female,164.1 -female,170.6 -female,160.0 -female,145.9 -female,158.9 -female,164.9 -female,162.3 -female,158.1 -female,168.0 -female,157.9 -female,154.6 -female,163.3 -female,165.6 -female,165.3 -female,161.3 -female,161.3 -female,166.0 -female,174.5 -female,148.1 -female,173.1 -female,157.6 -female,152.6 -female,162.5 -female,167.4 -female,148.1 -female,159.4 -female,163.0 -female,158.3 -female,162.0 -female,161.5 -female,163.2 -female,151.9 -female,148.1 -female,156.3 -female,172.1 -female,155.3 -female,157.7 -female,166.1 -female,154.0 -female,158.1 -female,165.5 -female,155.6 -female,169.7 -female,154.8 -female,165.3 -female,155.0 -female,161.6 -female,150.5 -female,143.3 -female,149.8 -female,150.6 -female,155.6 -female,171.4 -female,153.5 -female,153.4 -female,170.1 -female,158.0 -female,144.5 -female,157.0 -female,155.2 -female,159.4 -female,161.3 -female,155.4 -female,155.9 -female,156.8 -female,157.3 -female,171.6 -female,154.7 -female,157.8 -female,157.9 -female,169.2 -female,160.9 -female,148.3 -female,156.8 -female,158.3 -female,149.4 -female,165.7 -female,150.3 -female,165.5 -female,161.2 -female,166.4 -female,151.0 -female,169.1 -female,148.4 -female,153.4 -female,156.9 -female,154.3 -female,169.9 -female,150.6 -female,163.9 -female,156.9 -female,167.6 -female,159.2 -female,157.7 -female,157.3 -female,166.3 -female,167.5 -female,164.8 -female,155.5 -female,171.2 -female,160.7 -female,152.7 -female,151.9 -female,176.0 -female,156.0 -female,159.2 -female,161.8 -female,161.9 -female,152.9 -female,159.9 -female,160.3 -female,154.5 -female,157.0 -female,169.5 -female,143.8 -female,170.2 -female,150.5 -female,151.6 -female,163.4 -female,146.7 -female,165.6 -female,152.9 -female,167.3 -female,158.1 -female,155.1 -female,163.4 -female,157.8 -female,171.3 -female,158.2 -female,156.3 -female,152.8 -female,158.3 -female,150.9 -female,158.9 -female,166.5 -female,158.6 -female,145.9 -female,164.4 -female,157.9 -female,149.2 -female,154.5 -female,153.2 -female,166.4 -female,154.5 -female,162.7 -female,156.5 -female,159.7 -female,165.0 -female,163.7 -female,153.6 -female,166.7 -female,161.2 -female,148.6 -female,155.4 -female,162.3 -female,163.7 -female,160.6 -female,150.7 -female,165.3 -female,154.0 -female,161.6 -female,165.5 -female,149.5 -female,152.9 -female,160.1 -female,167.2 -female,156.3 -female,171.7 -female,147.3 -female,173.3 -female,155.3 -female,166.6 -female,173.6 -female,159.5 -female,158.6 -female,164.1 -female,158.8 -female,154.7 -female,161.0 -female,162.0 -female,174.5 -female,168.0 -female,149.5 -female,157.9 -female,146.7 -female,156.8 -female,156.6 -female,148.0 -female,157.5 -female,151.2 -female,157.9 -female,154.3 -female,159.1 -female,157.8 -female,155.5 -female,167.9 -female,158.3 -female,157.0 -female,153.7 -female,160.2 -female,158.6 -female,152.1 -female,170.9 -female,146.3 -female,156.0 -female,163.5 -female,159.5 -female,157.0 -female,158.7 -female,154.7 -female,155.0 -female,155.3 -female,155.3 -female,155.3 -female,161.5 -female,150.0 -female,170.5 -female,158.6 -female,163.7 -female,167.3 -female,154.2 -female,171.2 -female,154.1 -female,167.8 -female,148.0 -female,165.8 -female,153.2 -female,170.3 -female,166.5 -female,162.3 -female,159.0 -female,159.8 -female,158.8 -female,159.0 -female,154.7 -female,146.0 -female,159.4 -female,161.8 -female,165.2 -female,159.8 -female,160.1 -female,154.0 -female,160.6 -female,143.8 -female,150.8 -female,166.7 -female,154.2 -female,168.7 -female,163.9 -female,146.8 -female,161.8 -female,168.2 -female,154.3 -female,159.6 -female,151.3 -female,165.4 -female,166.8 -female,167.0 -female,146.1 -female,160.3 -female,157.3 -female,156.7 -female,155.7 -female,150.1 -female,163.7 -female,144.0 -female,165.0 -female,150.8 -female,168.4 -female,158.7 -female,164.5 -female,151.9 -female,178.1 -female,153.1 -female,168.2 -female,172.3 -female,163.1 -female,163.9 -female,166.9 -female,156.7 -female,156.8 -female,154.6 -female,155.4 -female,158.7 -female,165.6 -female,157.5 -female,163.9 -female,158.6 -female,167.8 -female,162.7 -female,164.8 -female,163.2 -female,143.0 -female,160.0 -female,160.5 -female,161.2 -female,168.1 -female,154.0 -female,163.6 -female,163.3 -female,163.9 -female,154.3 -female,159.6 -female,157.9 -female,166.4 -female,157.4 -female,153.5 -female,165.2 -female,152.8 -female,171.3 -female,156.2 -female,171.9 -female,162.3 -female,159.5 -female,160.3 -female,166.4 -female,160.2 -female,152.5 -female,160.9 -female,174.5 -female,167.3 -female,155.8 -female,165.9 -female,156.7 -female,157.1 -female,160.4 -female,152.7 -female,155.2 -female,152.4 -female,162.2 -female,157.9 -female,147.7 -female,164.7 -female,157.9 -female,156.4 -female,169.0 -female,144.2 -female,168.6 -female,152.7 -female,161.1 -female,156.7 -female,153.4 -female,164.9 -female,155.8 -female,148.7 -female,158.6 -female,156.8 -female,161.4 -female,156.6 -female,151.7 -female,158.7 -female,152.9 -female,160.9 -female,165.5 -female,159.8 -female,155.7 -female,168.4 -female,153.0 -female,159.8 -female,149.9 -female,173.7 -female,169.8 -female,154.1 -female,149.4 -female,165.9 -female,159.1 -female,168.7 -female,158.4 -female,165.1 -female,160.3 -female,159.5 -female,156.6 -female,153.9 -female,167.7 -female,172.0 -female,152.2 -female,158.0 -female,161.5 -female,154.2 -female,160.8 -female,151.7 -female,170.9 -female,165.1 -female,168.7 -female,160.6 -female,159.2 -female,164.9 -female,169.0 -female,152.2 -female,158.6 -female,163.2 -female,166.5 -female,150.0 -female,163.5 -female,156.3 -female,176.3 -female,167.3 -female,165.6 -female,167.7 -female,156.2 -female,158.0 -female,156.5 -female,150.0 -female,166.1 -female,171.3 -female,165.5 -female,162.8 -female,166.7 -female,154.0 -female,157.0 -female,155.6 -female,156.7 -female,147.4 -female,154.7 -female,166.8 -female,161.2 -female,163.6 -female,165.7 -female,152.5 -female,158.8 -female,164.0 -female,147.0 -female,168.8 -female,150.7 -female,153.9 -female,155.2 -female,165.3 -female,162.6 -female,158.0 -female,167.6 -female,161.1 -female,146.4 -female,150.4 -female,159.2 -female,150.2 -female,161.4 -female,168.2 -female,152.7 -female,164.5 -female,159.2 -female,149.4 -female,163.2 -female,164.0 -female,156.0 -female,156.5 -female,160.6 -female,158.3 -female,158.8 -female,159.1 -female,157.1 -female,164.4 -female,153.7 -female,160.2 -female,154.1 -female,152.1 -female,173.2 -female,163.5 -female,161.3 -female,168.6 -female,156.0 -female,129.7 -female,170.5 -female,160.1 -female,168.3 -female,157.4 -female,157.2 -female,153.3 -female,153.8 -female,161.5 -female,167.3 -female,161.7 -female,154.3 -female,144.7 -female,160.0 -female,150.3 -female,157.8 -female,168.6 -female,166.7 -female,158.9 -female,167.9 -female,150.7 -female,151.0 -female,147.7 -female,158.7 -female,154.7 -female,172.8 -female,159.6 -female,168.7 -female,158.2 -female,150.2 -female,163.1 -female,147.4 -female,155.4 -female,147.2 -female,160.1 -female,168.1 -female,170.6 -female,151.2 -female,163.4 -female,145.4 -female,162.4 -female,148.7 -female,164.2 -female,152.6 -female,172.0 -female,160.5 -female,158.2 -female,169.8 -female,150.8 -female,168.1 -female,162.9 -female,155.4 -female,163.8 -female,164.8 -female,156.6 -female,165.8 -female,153.1 -female,151.7 -female,172.6 -female,169.7 -female,171.7 -female,163.4 -female,153.3 -female,149.6 -female,150.6 -female,155.2 -female,144.2 -female,156.4 -female,165.4 -female,158.2 -female,158.9 -female,146.1 -female,154.7 -female,161.4 -female,155.1 -female,157.4 -female,157.4 -female,156.7 -female,156.1 -female,168.9 -female,156.2 -female,144.1 -female,159.5 -female,169.5 -female,173.3 -female,153.6 -female,160.8 -female,168.2 -female,168.0 -female,162.2 -female,153.5 -female,162.7 -female,157.5 -female,155.2 -female,155.1 -female,170.0 -female,159.4 -female,151.5 -female,156.8 -female,169.1 -female,156.9 -female,159.8 -female,151.3 -female,159.9 -female,150.1 -female,151.0 -female,166.7 -female,163.8 -female,153.0 -female,159.4 -female,151.8 -female,163.8 -female,150.1 -female,155.8 -female,158.9 -female,162.2 -female,164.8 -female,154.2 -female,150.0 -female,173.3 -female,156.7 -female,153.6 -female,156.3 -female,165.5 -female,159.6 -female,168.2 -female,145.4 -female,155.7 -female,159.5 -female,153.6 -female,169.0 -female,156.6 -female,162.3 -female,164.2 -female,154.4 -female,169.6 -female,151.7 -female,164.4 -female,160.8 -female,169.8 -female,171.4 -female,169.5 -female,161.2 -female,160.2 -female,167.5 -female,158.3 -female,164.4 -female,166.0 -female,157.9 -female,146.2 -female,155.6 -female,165.0 -female,162.4 -female,161.5 -female,153.1 -female,154.9 -female,172.3 -female,165.4 -female,163.7 -female,153.7 -female,164.6 -female,165.3 -female,154.9 -female,147.6 -female,156.4 -female,145.8 -female,166.7 -female,147.1 -female,155.5 -female,166.4 -female,164.9 -female,150.0 -female,159.8 -female,153.5 -female,163.3 -female,151.6 -female,164.9 -female,165.8 -female,161.7 -female,172.4 -female,169.4 -female,160.7 -female,155.2 -female,147.5 -female,163.2 -female,157.2 -female,175.2 -female,148.9 -female,155.3 -female,166.8 -female,153.5 -female,154.3 -female,156.6 -female,156.5 -female,169.3 -female,160.5 -female,166.8 -female,162.8 -female,155.2 -female,162.2 -female,161.7 -female,148.0 -female,170.5 -female,161.5 -female,154.0 -female,167.5 -female,155.6 -female,170.1 -female,156.5 -female,162.9 -female,148.0 -female,165.4 -female,156.3 -female,155.0 -female,161.5 -female,150.4 -female,153.0 -female,160.7 -female,155.8 -female,155.0 -female,154.7 -female,163.6 -female,153.0 -female,148.7 -female,154.2 -female,163.5 -female,159.6 -female,154.1 -female,156.3 -female,175.3 -female,149.9 -female,162.7 -female,167.6 -female,161.5 -female,158.0 -female,167.6 -female,174.1 -female,164.0 -female,148.0 -female,158.2 -female,156.3 -female,157.8 -female,158.7 -female,173.4 -female,158.4 -female,164.6 -female,157.7 -female,167.6 -female,159.5 -female,156.9 -female,163.3 -female,139.6 -female,159.1 -female,159.5 -female,154.6 -female,161.1 -female,153.5 -female,162.8 -female,165.6 -female,166.1 -female,162.7 -female,158.3 -female,160.5 -female,159.4 -female,153.0 -female,154.5 -female,158.9 -female,140.7 -female,156.9 -female,157.5 -female,163.5 -female,166.4 -female,159.6 -female,165.2 -female,165.0 -female,159.1 -female,153.9 -female,170.3 -female,158.4 -female,160.0 -female,164.4 -female,163.2 -female,159.4 -female,158.3 -female,162.4 -female,168.1 -female,150.5 -female,149.4 -female,162.8 -female,148.0 -female,167.7 -female,172.2 -female,170.5 -female,155.9 -female,152.1 -female,158.8 -female,168.0 -female,148.6 -female,159.5 -female,176.8 -female,166.3 -female,155.0 -female,158.7 -female,168.2 -female,163.4 -female,155.0 -female,165.7 -female,168.2 -female,154.4 -female,165.4 -female,165.4 -female,162.7 -female,168.3 -female,150.6 -female,160.0 -female,169.3 -female,164.3 -female,137.9 -female,161.0 -female,153.2 -female,154.9 -female,170.5 -female,171.4 -female,148.8 -female,166.4 -female,154.4 -female,164.1 -female,162.4 -female,182.6 -female,156.1 -female,169.9 -female,149.7 -female,163.5 -female,164.9 -female,157.1 -female,158.7 -female,156.6 -female,174.9 -female,160.4 -female,163.4 -female,160.3 -female,167.5 -female,170.1 -female,152.6 -female,163.8 -female,156.4 -female,155.5 -female,159.5 -female,160.1 -female,161.1 -female,155.9 -female,159.0 -female,153.2 -female,167.0 -female,161.3 -female,156.0 -female,165.5 -female,162.7 -female,147.5 -female,175.6 -female,161.8 -female,171.0 -female,150.4 -female,155.9 -female,165.8 -female,152.1 -female,157.2 -female,157.8 -female,157.7 -female,159.7 -female,162.1 -female,159.4 -female,169.5 -female,154.6 -female,157.3 -female,156.3 -female,163.2 -female,154.7 -female,168.9 -female,162.9 -female,163.5 -female,156.5 -female,164.4 -female,149.3 -female,170.5 -female,164.4 -female,168.5 -female,157.3 -female,144.2 -female,157.4 -female,171.4 -female,160.2 -female,157.0 -female,168.8 -female,160.1 -female,150.4 -female,155.9 -female,152.5 -female,151.8 -female,171.9 -female,152.1 -female,156.9 -female,166.7 -female,153.9 -female,163.9 -female,160.6 -female,159.5 -female,167.9 -female,160.0 -female,171.2 -female,160.8 -female,156.0 -female,142.5 -female,167.8 -female,163.0 -female,162.7 -female,161.8 -female,159.6 -female,154.6 -female,160.1 -female,156.0 -female,165.0 -female,154.6 -female,166.6 -female,156.1 -female,164.5 -female,154.6 -female,163.9 -female,163.4 -female,151.7 -female,157.0 -female,153.7 -female,167.9 -female,153.4 -female,164.3 -female,154.3 -female,164.3 -female,155.9 -female,151.3 -female,165.9 -female,161.3 -female,171.1 -female,153.2 -female,171.8 -female,158.5 -female,161.3 -female,161.7 -female,156.5 -female,161.6 -female,148.2 -female,152.1 -female,158.6 -female,168.7 -female,146.8 -female,165.7 -female,180.3 -female,150.1 -female,153.0 -female,167.8 -female,176.6 -female,166.1 -female,168.1 -female,161.7 -female,150.7 -female,151.4 -female,174.8 -female,147.1 -female,158.6 -female,160.4 -female,165.5 -female,151.4 -female,156.9 -female,158.3 -female,158.5 -female,149.9 -female,162.2 -female,177.1 -female,164.5 -female,167.2 -female,147.6 -female,164.3 -female,158.4 -female,165.1 -female,162.5 -female,148.8 -female,162.2 -female,158.1 -female,157.0 -female,153.4 -female,176.6 -female,160.1 -female,158.4 -female,161.7 -female,158.3 -female,166.7 -female,166.3 -female,162.1 -female,160.5 -female,158.4 -female,165.9 -female,162.6 -female,159.3 -female,151.9 -female,163.4 -female,155.9 -female,166.3 -female,160.2 -female,164.6 -female,163.4 -female,149.8 -female,149.1 -female,168.0 -female,158.7 -female,160.5 -female,153.2 -female,147.5 -female,154.3 -female,163.1 -female,169.6 -female,155.0 -female,170.4 -female,157.5 -female,154.9 -female,162.7 -female,154.9 -female,150.2 -female,157.1 -female,162.8 -female,150.2 -female,158.4 -female,167.7 -female,166.8 -female,166.5 -female,170.4 -female,154.7 -female,153.8 -female,156.9 -female,155.7 -female,160.0 -female,164.3 -female,171.0 -female,166.0 -female,168.2 -female,149.9 -female,152.5 -female,149.7 -female,155.9 -female,164.8 -female,151.4 -female,162.0 -female,156.6 -female,154.9 -female,158.9 -female,147.8 -female,179.6 -female,162.9 -female,171.6 -female,165.9 -female,158.5 -female,160.1 -female,153.8 -female,170.3 -female,166.3 -female,162.4 -female,156.7 -female,150.3 -female,168.8 -female,160.9 -female,158.7 -female,159.8 -female,160.2 -female,153.6 -female,162.4 -female,146.4 -female,175.6 -female,159.6 -female,161.2 -female,160.9 -female,151.8 -female,156.4 -female,154.4 -female,163.0 -female,160.9 -female,158.6 -female,155.6 -female,159.6 -female,167.5 -female,170.5 -female,152.6 -female,155.4 -female,165.4 -female,158.3 -female,144.9 -female,150.0 -female,161.3 -female,147.2 -female,160.3 -female,161.9 -female,149.1 -female,157.7 -female,148.5 -female,166.8 -female,149.5 -female,172.3 -female,162.8 -female,157.5 -female,166.5 -female,158.0 -female,170.3 -female,147.3 -female,165.7 -female,163.9 -female,159.2 -female,167.6 -female,159.4 -female,169.9 -female,151.4 -female,150.1 -female,161.5 -female,158.2 -female,165.3 -female,153.9 -female,152.2 -female,157.0 -female,163.3 -female,147.1 -female,153.6 -female,167.1 -female,166.8 -female,153.7 -female,156.2 -female,160.7 -female,165.8 -female,163.3 -female,160.3 -female,156.5 -female,162.9 -female,157.1 -female,147.6 -female,175.2 -female,171.1 -female,156.9 -female,151.7 -female,171.5 -female,158.7 -female,150.9 -female,151.9 -female,160.6 -female,151.1 -female,151.7 -female,162.7 -female,172.9 -female,156.3 -female,167.9 -female,158.5 -female,160.3 -female,156.5 -female,167.2 -female,153.6 -female,153.2 -female,160.9 -female,160.8 -female,165.1 -female,159.8 -female,164.9 -female,160.2 -female,154.9 -female,165.4 -female,154.7 -female,164.3 -female,159.9 -female,165.4 -female,166.4 -female,166.1 -female,157.8 -female,161.9 -female,167.0 -female,160.3 -female,164.7 -female,155.6 -female,144.2 -female,161.8 -female,160.5 -female,156.5 -female,170.8 -female,155.6 -female,159.7 -female,158.4 -female,174.6 -female,154.6 -female,153.7 -female,166.3 -female,148.7 -female,159.4 -female,165.9 -female,167.2 -female,155.4 -female,153.9 -female,157.6 -female,173.8 -female,167.3 -female,167.1 -female,151.7 -female,165.7 -female,175.4 -female,176.7 -female,167.8 -female,149.2 -female,160.5 -female,162.0 -female,149.0 -female,160.9 -female,160.8 -female,175.9 -female,149.1 -female,152.5 -female,162.6 -female,150.1 -female,159.1 -female,155.5 -female,163.9 -female,161.2 -female,166.2 -female,165.7 -female,158.1 -female,170.9 -female,156.1 -female,160.7 -female,147.8 -female,158.9 -female,164.9 -female,162.6 -female,155.6 -female,159.5 -female,155.6 -female,145.7 -female,161.0 -female,168.2 -female,163.3 -female,169.3 -female,163.1 -female,172.8 -female,165.9 -female,159.0 -female,161.4 -female,151.6 -female,155.4 -female,144.7 -female,168.8 -female,149.4 -female,143.4 -female,155.9 -female,153.2 -female,162.7 -female,167.0 -female,153.1 -female,151.5 -female,162.5 -female,145.9 -female,166.0 -female,164.5 -female,163.4 -female,158.0 -female,158.2 -female,162.5 -female,168.4 -female,158.8 -female,161.2 -female,159.8 -female,157.8 -female,148.8 -female,150.8 -female,159.8 -female,157.5 -female,156.6 -female,158.3 -female,163.7 -female,174.6 -female,148.9 -female,160.8 -female,137.4 -female,176.9 -female,169.1 -female,144.3 -female,169.6 -female,154.2 -female,159.2 -female,154.5 -female,160.2 -female,158.5 -female,148.9 -female,155.2 -female,155.9 -female,166.7 -female,150.3 -female,143.7 -female,156.3 -female,167.1 -female,162.9 -female,161.8 -female,143.1 -female,163.6 -female,161.8 -female,151.2 -female,161.0 -female,151.2 -female,157.7 -female,169.2 -female,150.2 -female,155.0 -female,159.2 -female,152.1 -female,166.1 -female,149.6 -female,160.1 -female,157.8 -female,173.0 -female,163.0 -female,166.4 -female,158.6 -female,161.3 -female,170.4 -female,152.5 -female,161.7 -female,168.9 -female,143.7 -female,154.0 -female,167.1 -female,172.1 -female,151.2 -female,159.7 -female,149.1 -female,157.8 -female,166.3 -female,156.6 -female,156.6 -female,155.3 -female,160.0 -female,166.1 -female,150.5 -female,165.9 -female,157.7 -female,163.0 -female,153.6 -female,168.7 -female,156.9 -female,169.8 -female,165.9 -female,164.0 -female,149.2 -female,161.9 -female,155.8 -female,155.4 -female,162.2 -female,157.4 -female,154.8 -female,165.9 -female,159.5 -female,160.6 -female,148.0 -female,153.0 -female,154.6 -female,161.8 -female,166.9 -female,161.9 -female,153.6 -female,161.0 -female,161.0 -female,169.3 -female,151.9 -female,159.2 -female,151.7 -female,165.7 -female,159.6 -female,145.4 -female,149.3 -female,175.1 -female,154.1 -female,160.1 -female,157.5 -female,158.9 -female,158.2 -female,156.2 -female,159.2 -female,163.4 -female,150.6 -female,153.4 -female,155.2 -female,164.7 -female,148.7 -female,158.3 -female,162.7 -female,161.7 -female,157.7 -female,168.2 -female,153.3 -female,163.9 -female,160.3 -female,159.4 -female,159.5 -female,146.5 -female,160.2 -female,152.5 -female,155.7 -female,152.5 -female,154.2 -female,172.9 -female,168.0 -female,155.7 -female,155.8 -female,169.4 -female,160.7 -female,168.0 -female,163.3 -female,172.5 -female,161.0 -female,151.6 -female,156.3 -female,167.4 -female,152.6 -female,162.5 -female,157.8 -female,147.0 -female,160.8 -female,161.6 -female,150.3 -female,163.9 -female,167.3 -female,163.2 -female,157.7 -female,168.5 -female,159.7 -female,143.1 -female,160.1 -female,158.2 -female,149.9 -female,157.0 -female,171.2 -female,165.1 -female,162.9 -female,160.0 -female,155.1 -female,156.3 -female,153.8 -female,157.1 -female,163.3 -female,154.5 -female,156.2 -female,154.7 -female,164.7 -female,159.7 -female,162.4 -female,150.2 -female,160.5 -female,165.6 -female,166.6 -female,171.7 -female,163.2 -female,144.9 -female,166.8 -female,160.8 -female,161.4 -female,158.5 -female,157.4 -female,154.0 -female,156.9 -female,168.1 -female,161.4 -female,154.9 -female,154.7 -female,160.1 -female,162.8 -female,158.7 -female,158.7 -female,157.9 -female,158.8 -female,150.0 -female,173.3 -female,158.8 -female,150.0 -female,158.6 -female,164.6 -female,161.0 -female,158.0 -female,158.7 -female,156.8 -female,162.1 -female,175.0 -female,168.9 -female,162.1 -female,159.9 -female,145.9 -female,166.2 -female,160.2 -female,159.9 -female,156.3 -female,165.4 -female,173.5 -female,156.7 -female,153.9 -female,160.3 -female,158.1 -female,151.5 -female,159.7 -female,164.8 -female,144.4 -female,156.3 -female,163.8 -female,162.8 -female,151.5 -female,162.5 -female,158.0 -female,148.6 -female,172.9 -female,162.5 -female,156.0 -female,156.9 -female,175.3 -female,167.4 -female,160.6 -female,154.4 -female,161.6 -female,165.6 -female,155.1 -female,165.9 -female,160.4 -female,155.3 -female,159.9 -female,166.2 -female,171.7 -female,156.1 -female,151.6 -female,165.6 -female,154.4 -female,147.9 -female,156.7 -female,155.1 -female,165.6 -female,159.1 -female,157.3 -female,163.0 -female,141.1 -female,173.7 -female,152.7 -female,157.9 -female,153.5 -female,160.2 -female,163.7 -female,157.1 -female,158.9 -female,166.2 -female,145.2 -female,167.2 -female,158.8 -female,165.3 -female,166.1 -female,157.0 -female,158.2 -female,152.0 -female,152.5 -female,154.1 -female,159.0 -female,162.5 -female,157.9 -female,155.8 -female,162.6 -female,155.4 -female,164.0 -female,159.1 -female,154.1 -female,161.3 -female,153.2 -female,151.0 -female,157.9 -female,169.4 -female,157.7 -female,164.3 -female,163.3 -female,161.8 -female,160.3 -female,167.2 -female,157.8 -female,168.1 -female,152.2 -female,168.2 -female,150.7 -female,169.5 -female,146.2 -female,154.9 -female,165.5 -female,158.4 -female,165.5 -female,156.5 -female,148.4 -female,159.0 -female,163.4 -female,159.3 -female,169.8 -female,148.4 -female,174.4 -female,165.1 -female,161.4 -female,147.3 -female,165.6 -female,152.6 -female,145.8 -female,154.0 -female,168.4 -female,149.0 -female,154.6 -female,166.7 -female,163.3 -female,145.9 -female,159.8 -female,148.0 -female,158.2 -female,158.7 -female,161.2 -female,158.2 -female,157.5 -female,170.1 -female,170.6 -female,157.6 -female,150.5 -female,150.5 -female,156.9 -female,163.8 -female,147.0 -female,155.6 -female,155.7 -female,163.6 -female,150.1 -female,153.2 -female,167.0 -female,173.5 -female,155.8 -female,149.8 -female,160.9 -female,152.7 -female,154.2 -female,162.3 -female,159.5 -female,161.2 -female,159.7 -female,170.5 -female,169.9 -female,161.8 -female,160.6 -female,159.5 -female,158.1 -female,162.5 -female,169.6 -female,158.5 -female,165.7 -female,163.1 -female,170.1 -female,152.9 -female,167.9 -female,159.6 -female,160.3 -female,153.0 -female,159.5 -female,155.5 -female,154.7 -female,160.6 -female,149.8 -female,170.6 -female,147.4 -female,152.7 -female,168.8 -female,157.1 -female,168.5 -female,159.3 -female,158.6 -female,158.3 -female,158.8 -female,152.9 -female,157.8 -female,154.9 -female,155.0 -female,159.5 -female,152.8 -female,172.7 -female,168.8 -female,154.4 -female,151.6 -female,153.3 -female,161.9 -female,163.4 -female,154.0 -female,156.7 -female,145.9 -female,166.1 -female,163.5 -female,155.5 -female,145.3 -female,147.6 -female,151.2 -female,167.9 -female,163.0 -female,155.0 -female,149.4 -female,160.7 -female,169.6 -female,163.3 -female,162.5 -female,166.4 -female,158.8 -female,167.7 -female,150.5 -female,152.2 -female,158.0 -female,165.8 -female,155.7 -female,165.1 -female,154.8 -female,162.2 -female,172.9 -female,166.5 -female,163.4 -female,153.2 -female,163.2 -female,166.8 -female,158.9 -female,154.4 -female,151.6 -female,162.6 -female,155.2 -female,168.6 -female,152.6 -female,148.5 -female,158.4 -female,156.3 -female,165.2 -female,164.5 -female,156.9 -female,165.0 -female,147.3 -female,157.0 -female,170.1 -female,163.1 -female,153.6 -female,154.4 -female,139.0 -female,162.9 -female,153.9 -female,160.5 -female,155.1 -female,169.7 -female,146.8 -female,154.7 -female,158.5 -female,155.1 -female,167.0 -female,151.5 -female,159.4 -female,161.0 -female,164.9 -female,159.6 -female,155.6 -female,150.9 -female,158.2 -female,160.5 -female,148.6 -female,163.5 -female,152.4 -female,169.7 -female,170.4 -female,155.6 -female,154.0 -female,169.5 -female,159.9 -female,160.3 -female,149.4 -female,160.8 -female,163.6 -female,163.1 -female,163.2 -female,154.6 -female,161.2 -female,161.8 -female,156.9 -female,169.1 -female,171.8 -female,165.5 -female,144.4 -female,157.4 -female,162.3 -female,156.2 -female,154.9 -female,169.5 -female,149.1 -female,162.6 -female,167.2 -female,170.2 -female,167.9 -female,159.3 -female,164.4 -female,155.5 -female,158.1 -female,166.7 -female,158.6 -female,147.1 -female,158.9 -female,163.1 -female,166.1 -female,177.0 -female,154.4 -female,168.4 -female,159.3 -female,155.3 -female,161.6 -female,157.0 -female,161.0 -female,152.5 -female,155.4 -female,155.1 -female,165.4 -female,159.8 -female,158.3 -female,163.0 -female,161.8 -female,151.9 -female,151.8 -female,167.7 -female,155.9 -female,153.5 -female,163.8 -female,150.7 -female,154.6 -female,143.0 -female,176.7 -female,172.0 -female,164.0 -female,161.2 -female,149.5 -female,163.4 -female,163.8 -female,151.3 -female,171.1 -female,138.4 -female,163.7 -female,152.8 -female,163.2 -female,169.3 -female,144.9 -female,155.3 -female,159.9 -female,161.8 -female,169.4 -female,157.5 -female,166.6 -female,159.8 -female,164.0 -female,160.6 -female,173.4 -female,160.6 -female,152.5 -female,161.2 -female,168.2 -female,150.7 -female,157.9 -female,153.4 -female,165.4 -female,157.8 -female,163.0 -female,151.9 -female,161.4 -female,154.7 -female,163.7 -female,159.4 -female,150.6 -female,145.1 -female,146.8 -female,160.0 -female,159.4 -female,152.9 -female,153.8 -female,152.5 -female,161.8 -female,165.6 -female,160.7 -female,178.0 -female,149.2 -female,154.0 -female,164.7 -female,175.4 -female,168.2 -female,165.2 -female,167.4 -female,152.7 -female,172.8 -female,144.9 -female,169.1 -female,157.1 -female,163.6 -female,156.0 -female,165.3 -female,153.6 -female,157.2 -female,162.0 -female,152.3 -female,156.5 -female,168.1 -female,161.7 -female,152.3 -female,164.7 -female,163.0 -female,148.1 -female,140.0 -female,168.8 -female,157.6 -female,158.5 -female,152.4 -female,155.9 -female,167.8 -female,159.2 -female,160.5 -female,164.5 -female,161.0 -female,158.9 -female,151.6 -female,146.4 -female,163.0 -female,153.7 -female,164.9 -female,177.6 -female,163.8 -female,149.6 -female,162.8 -female,151.7 -female,161.9 -female,170.4 -female,161.5 -female,148.9 -female,155.8 -female,154.5 -female,161.3 -female,147.1 -female,169.5 -female,162.3 -female,165.4 -female,156.6 -female,166.6 -female,162.1 -female,152.2 -female,159.7 -female,148.9 -female,162.6 -female,160.2 -female,154.8 -female,158.4 -female,170.8 -female,170.7 -female,163.0 -female,164.8 -female,163.6 -female,153.5 -female,156.2 -female,184.1 -female,174.3 -female,161.0 -female,161.3 -female,166.2 -female,158.1 -female,162.4 -female,159.0 -female,149.1 -female,158.8 -female,167.7 -female,162.4 -female,161.8 -female,161.6 -female,161.2 -female,161.9 -female,154.5 -female,154.7 -female,163.7 -female,162.2 -female,154.7 -female,167.2 -female,170.9 -female,169.0 -female,167.1 -female,158.6 -female,152.1 -female,153.9 -female,151.3 -female,151.4 -female,172.2 -female,167.2 -female,156.3 -female,159.1 -female,167.0 -female,161.1 -female,172.3 -female,164.7 -female,164.9 -female,144.6 -female,172.6 -female,167.1 -female,160.9 -female,162.7 -female,164.5 -female,161.6 -female,163.6 -female,167.1 -female,153.9 -female,155.7 -female,170.2 -female,160.2 -female,162.3 -female,169.4 -female,163.4 -female,157.1 -female,154.2 -female,170.1 -female,162.0 -female,161.0 -female,146.2 -female,163.4 -female,139.0 -female,165.2 -female,153.1 -female,145.3 -female,163.6 -female,166.2 -female,159.2 -female,169.9 -female,167.3 -female,163.7 -female,160.8 -female,170.7 -female,169.0 -female,157.7 -female,169.2 -female,159.3 -female,158.2 -female,168.7 -female,151.2 -female,154.1 -female,153.9 -female,147.9 -female,143.0 -female,155.7 -female,157.4 -female,159.6 -female,159.4 -female,164.9 -female,161.5 -female,153.9 -female,148.3 -female,160.6 -female,150.6 -female,162.0 -female,156.2 -female,152.4 -female,159.4 -female,158.6 -female,168.8 -female,161.8 -female,149.7 -female,152.2 -female,159.9 -female,153.6 -female,169.9 -female,152.2 -female,137.6 -female,158.1 -female,150.2 -female,161.3 -female,165.5 -female,158.9 -female,156.3 -female,164.8 -female,160.7 -female,177.0 -female,149.5 -female,159.6 -female,149.5 -female,158.8 -female,153.0 -female,147.6 -female,183.4 -female,153.8 -female,156.9 -female,146.1 -female,154.4 -female,153.9 -female,150.7 -female,169.7 -female,150.3 -female,156.4 -female,156.2 -female,150.1 -female,150.1 -female,150.9 -female,169.3 -female,151.1 -female,157.1 -female,163.4 -female,163.4 -female,158.3 -female,148.2 -female,169.9 -female,156.4 -female,170.8 -female,154.7 -female,162.2 -female,144.1 -female,160.2 -female,162.4 -female,155.6 -female,163.0 -female,153.3 -female,161.8 -female,164.0 -female,171.8 -female,161.6 -female,170.0 -female,160.1 -female,164.4 -female,166.2 -female,152.4 -female,180.0 -female,151.6 -female,169.3 -female,161.3 -female,158.1 -female,174.1 -female,153.3 -female,167.0 -female,155.2 -female,168.1 -female,158.2 -female,153.9 -female,163.2 -female,153.1 -female,159.5 -female,157.3 -female,159.0 -female,155.0 -female,170.9 -female,165.5 -female,154.6 -female,150.6 -female,162.3 -female,140.3 -female,154.9 -female,150.5 -female,160.9 -female,155.8 -female,164.2 -female,164.6 -female,147.8 -female,154.2 -female,160.3 -female,145.1 -female,157.7 -female,148.8 -female,148.8 -female,155.0 -female,156.2 -female,169.1 -female,167.0 -female,167.5 -female,160.7 -female,162.6 -female,163.3 -female,156.5 -female,146.1 -female,159.3 -female,156.5 -female,147.5 -female,165.5 -female,160.4 -female,170.6 -female,145.8 -female,161.8 -female,156.4 -female,159.4 -female,147.2 -female,170.6 -female,172.1 -female,154.6 -female,182.3 -female,166.4 -female,153.7 -female,148.9 -female,163.9 -female,161.8 -female,157.5 -female,143.6 -female,151.7 -female,172.9 -female,143.2 -female,167.2 -female,153.0 -female,159.8 -female,162.0 -female,156.7 -female,145.5 -female,156.6 -female,160.4 -female,164.1 -female,158.7 -female,166.7 -female,142.0 -female,158.7 -female,161.0 -female,167.3 -female,155.6 -female,153.8 -female,160.3 -female,145.2 -female,155.6 -female,160.6 -female,163.9 -female,161.2 -female,144.3 -female,162.8 -female,170.3 -female,153.2 -female,153.0 -female,161.3 -female,153.5 -female,161.7 -female,164.7 -female,157.5 -female,154.0 -female,166.9 -female,163.6 -female,169.7 -female,169.2 -female,158.5 -female,160.8 -female,169.1 -female,163.4 -female,163.1 -female,151.0 -female,166.2 -female,162.0 -female,151.2 -female,160.2 -female,155.7 -female,161.5 -female,157.3 -female,153.7 -female,166.7 -female,154.6 -female,170.6 -female,161.4 -female,150.8 -female,162.1 -female,167.5 -female,149.8 -female,164.7 -female,165.8 -female,164.0 -female,158.9 -female,157.7 -female,169.8 -female,169.7 -female,169.9 -female,149.7 -female,170.1 -female,159.9 -female,157.2 -female,152.4 -female,160.4 -female,163.6 -female,170.8 -female,164.1 -female,155.5 -female,162.5 -female,157.8 -female,159.3 -female,148.6 -female,157.7 -female,156.5 -female,151.6 -female,165.5 -female,146.1 -female,143.1 -female,168.3 -female,166.6 -female,165.1 -female,162.8 -female,159.7 -female,155.5 -female,172.5 -female,146.7 -female,159.9 -female,158.1 -female,144.9 -female,157.8 -female,168.4 -female,166.7 -female,150.6 -female,166.7 -female,170.0 -female,160.1 -female,146.4 -female,165.5 -female,161.1 -female,167.5 -female,172.4 -female,160.5 -female,176.3 -female,157.1 -female,155.3 -female,160.3 -female,161.9 -female,152.5 -female,160.7 -female,161.1 -female,164.3 -female,175.6 -female,158.3 -female,154.5 -female,168.2 -female,154.5 -female,148.2 -female,169.0 -female,168.7 -female,147.3 -female,166.9 -female,162.6 -female,162.8 -female,160.8 -female,167.0 -female,160.9 -female,160.3 -female,170.4 -female,155.1 -female,160.2 -female,155.2 -female,154.5 -female,167.9 -female,152.8 -female,162.3 -female,152.6 -female,163.1 -female,151.6 -female,165.8 -female,157.3 -female,159.3 -female,168.5 -female,168.9 -female,167.8 -female,164.0 -female,148.7 -female,164.4 -female,161.9 -female,160.9 -female,150.5 -female,178.7 -female,165.6 -female,165.8 -female,146.0 -female,149.3 -female,149.7 -female,169.6 -female,148.3 -female,174.2 -female,147.4 -female,154.1 -female,153.2 -female,161.0 -female,145.7 -female,157.4 -female,150.0 -female,170.9 -female,162.9 -female,165.6 -female,152.4 -female,167.3 -female,151.2 -female,159.7 -female,158.4 -female,158.6 -female,162.1 -female,165.2 -female,154.6 -female,148.9 -female,156.8 -female,163.2 -female,166.1 -female,165.9 -female,154.5 -female,164.9 -female,149.9 -female,162.3 -female,154.7 -female,165.1 -female,171.4 -female,157.1 -female,158.5 -female,154.3 -female,150.4 -female,160.5 -female,150.1 -female,171.2 -female,154.8 -female,162.0 -female,161.2 -female,156.3 -female,156.7 -female,149.9 -female,166.5 -female,162.4 -female,163.2 -female,162.5 -female,174.0 -female,156.9 -female,164.6 -female,155.5 -female,154.9 -female,150.2 -female,169.0 -female,165.9 -female,158.0 -female,166.3 -female,166.6 -female,152.7 -female,157.8 -female,154.5 -female,159.0 -female,153.7 -female,156.0 -female,167.3 -female,148.0 -female,165.3 -female,161.7 -female,156.2 -female,161.7 -female,158.1 -female,160.9 -female,152.5 -female,153.5 -female,168.8 -female,154.2 -female,166.6 -female,169.7 -female,160.9 -female,149.8 -female,158.0 -female,152.4 -female,181.5 -female,170.0 -female,164.0 -female,161.3 -female,159.4 -female,159.2 -female,153.6 -female,153.5 -female,173.8 -female,170.6 -female,166.1 -female,162.4 -female,149.9 -female,149.3 -female,152.7 -female,160.3 -female,145.6 -female,158.5 -female,166.8 -female,169.3 -female,152.6 -female,156.4 -female,157.6 -female,169.6 -female,149.0 -female,147.6 -female,161.7 -female,167.4 -female,157.0 -female,166.9 -female,151.9 -female,165.8 -female,152.2 -female,165.0 -female,158.3 -female,150.2 -female,151.1 -female,147.8 -female,154.0 -female,154.6 -female,154.5 -female,158.4 -female,153.6 -female,178.5 -female,160.7 -female,156.9 -female,150.6 -female,149.8 -female,156.6 -female,161.9 -female,165.5 -female,150.4 -female,157.8 -female,161.7 -female,164.7 -female,156.9 -female,155.0 -female,169.5 -female,173.4 -female,160.4 -female,157.1 -female,164.3 -female,173.0 -female,162.8 -female,162.9 -female,155.3 -female,168.9 -female,161.5 -female,143.7 -female,159.8 -female,159.4 -female,161.9 -female,161.4 -female,161.7 -female,166.8 -female,177.4 -female,171.5 -female,163.8 -female,165.3 -female,165.9 -female,156.6 -female,164.6 -female,155.6 -female,149.1 -female,171.0 -female,158.1 -female,158.8 -female,162.5 -female,164.7 -female,167.6 -female,145.4 -female,167.0 -female,162.3 -female,158.2 -female,173.7 -female,162.0 -female,160.2 -female,160.3 -female,154.2 -female,151.8 -female,156.1 -female,158.6 -female,153.3 -female,169.4 -female,146.7 -female,150.7 -female,161.7 -female,166.5 -female,171.0 -female,159.5 -female,163.9 -female,161.4 -female,162.1 -female,173.8 -female,157.3 -female,171.4 -female,143.6 -female,160.7 -female,146.9 -female,163.6 -female,163.1 -female,158.4 -female,159.1 -female,166.7 -female,158.2 -female,159.2 -female,160.6 -female,164.8 -female,159.8 -female,163.2 -female,159.8 -female,148.7 -female,166.8 -female,166.2 -female,159.7 -female,144.5 -female,162.5 -female,167.2 -female,157.5 -female,162.3 -female,143.7 -female,171.2 -female,155.3 -female,156.6 -female,161.5 -female,158.4 -female,145.4 -female,154.2 -female,151.4 -female,163.2 -female,158.1 -female,148.8 -female,159.0 -female,151.7 -female,160.1 -female,163.2 -female,155.2 -female,158.0 -female,162.7 -female,159.0 -female,167.4 -female,165.3 -female,163.7 -female,155.0 -female,160.4 -female,163.7 -female,169.1 -female,156.2 -female,163.2 -female,153.3 -female,152.9 -female,163.3 -female,160.8 -female,145.7 -female,150.9 -female,148.4 -female,176.7 -female,157.8 -female,153.1 -female,148.8 -female,162.1 -female,145.7 -female,156.4 -female,158.2 -female,144.7 -female,158.3 -female,154.0 -female,168.8 -female,155.4 -female,155.4 -female,153.5 -female,160.4 -female,162.8 -female,148.5 -female,162.0 -female,155.6 -female,154.0 -female,167.0 -female,152.3 -female,151.6 -female,164.6 -female,161.8 -female,163.6 -female,166.7 -female,162.0 -female,160.0 -female,166.6 -female,147.0 -female,164.6 -female,153.3 -female,173.3 -female,151.2 -female,171.1 -female,162.5 -female,172.7 -female,165.0 -female,154.5 -female,147.2 -female,157.4 -female,166.2 -female,151.7 -female,170.2 -female,165.1 -female,173.1 -female,159.0 -female,147.0 -female,156.1 -female,154.5 -female,160.3 -female,163.5 -female,153.5 -female,160.7 -female,158.8 -female,156.3 -female,159.7 -female,157.9 -female,163.4 -female,165.1 -female,165.6 -female,161.4 -female,163.5 -female,165.4 -female,155.0 -female,167.2 -female,152.1 -female,156.6 -female,159.1 -female,161.5 -female,151.6 -female,177.7 -female,153.6 -female,162.9 -female,143.6 -female,159.3 -female,157.7 -female,155.2 -female,172.1 -female,161.8 -female,158.6 -female,174.9 -female,173.6 -female,165.7 -female,166.4 -female,164.6 -female,160.6 -female,153.7 -female,162.1 -female,163.3 -female,161.3 -female,162.4 -female,141.5 -female,170.8 -female,151.7 -female,163.6 -female,155.5 -female,162.0 -female,160.1 -female,176.7 -female,159.3 -female,157.3 -female,168.7 -female,162.8 -female,173.6 -female,152.3 -female,151.7 -female,168.2 -female,158.2 -female,155.4 -female,148.3 -female,158.2 -female,157.9 -female,157.6 -female,155.1 -female,165.8 -female,164.8 -female,151.3 -female,156.4 -female,150.6 -female,156.8 -female,147.7 -female,171.1 -female,154.6 -female,168.4 -female,161.1 -female,152.7 -female,167.4 -female,153.5 -female,161.4 -female,159.0 -female,175.9 -female,165.1 -female,146.8 -female,163.5 -female,164.1 -female,176.4 -female,161.9 -female,165.0 -female,166.5 -female,163.8 -female,165.8 -female,153.8 -female,152.5 -female,151.5 -female,160.3 -female,163.3 -female,148.1 -female,157.9 -female,155.5 -female,142.9 -female,164.0 -female,157.4 -female,160.2 -female,176.8 -female,157.4 -female,165.3 -female,165.3 -female,171.9 -female,164.7 -female,164.2 -female,172.5 -female,158.0 -female,165.4 -female,158.4 -female,169.1 -female,159.7 -female,168.5 -female,147.8 -female,161.6 -female,159.6 -female,159.4 -female,165.0 -female,159.8 -female,146.2 -female,169.0 -female,153.0 -female,172.6 -female,176.3 -female,155.3 -female,158.8 -female,160.8 -female,154.2 -female,155.6 -female,148.3 -female,160.1 -female,169.5 -female,164.9 -female,159.3 -female,155.5 -female,164.7 -female,158.2 -female,160.0 -female,153.3 -female,163.5 -female,153.5 -female,153.0 -female,166.3 -female,145.6 -female,167.0 -female,160.1 -female,157.1 -female,162.5 -female,156.1 -female,154.0 -female,165.8 -female,160.0 -female,154.1 -female,159.0 -female,171.7 -female,161.0 -female,168.7 -female,151.9 -female,163.3 -female,171.5 -female,175.1 -female,158.3 -female,148.5 -female,162.5 -female,165.0 -female,173.5 -female,165.3 -female,153.9 -female,161.0 -female,152.1 -female,151.3 -female,171.1 -female,161.1 -female,152.5 -female,151.1 -female,158.1 -female,154.4 -female,155.9 -female,161.7 -female,159.1 -female,163.6 -female,156.5 -female,149.3 -female,141.4 -female,155.6 -female,155.3 -female,155.1 -female,157.2 -female,163.5 -female,171.6 -female,159.0 -female,156.7 -female,168.3 -female,163.3 -female,144.4 -female,159.1 -female,150.6 -female,160.3 -female,162.0 -female,147.6 -female,149.3 -female,165.5 -female,169.1 -female,154.7 -female,158.3 -female,160.3 -female,144.1 -female,153.9 -female,158.9 -female,162.3 -female,163.7 -female,171.3 -female,160.4 -female,144.9 -female,168.2 -female,158.0 -female,161.1 -female,158.3 -female,149.2 -female,163.3 -female,163.0 -female,148.9 -female,173.0 -female,163.9 -female,143.3 -female,151.5 -female,161.4 -female,150.6 -female,159.6 -female,156.5 -female,161.1 -female,160.7 -female,157.1 -female,150.6 -female,152.8 -female,159.1 -female,151.1 -female,169.1 -female,153.1 -female,163.0 -female,154.2 -female,161.5 -female,153.0 -female,153.7 -female,158.4 -female,172.4 -female,161.3 -female,172.8 -female,145.4 -female,163.4 -female,168.5 -female,155.1 -female,158.2 -female,155.0 -female,161.6 -female,158.4 -female,158.4 -female,155.9 -female,143.7 -female,161.8 -female,153.3 -female,173.5 -female,163.1 -female,170.0 -female,174.9 -female,151.8 -female,163.8 -female,154.2 -female,156.8 -female,154.7 -female,157.5 -female,150.5 -female,155.9 -female,152.8 -female,153.9 -female,164.5 -female,157.9 -female,164.8 -female,162.0 -female,161.7 -female,157.6 -female,157.5 -female,158.8 -female,165.8 -female,154.5 -female,160.5 -female,148.5 -female,162.9 -female,160.9 -female,168.1 -female,153.5 -female,164.6 -female,153.9 -female,162.4 -female,147.6 -female,146.5 -female,166.2 -female,159.6 -female,155.6 -female,165.5 -female,152.7 -female,175.1 -female,147.2 -female,159.9 -female,163.7 -female,157.9 -female,163.8 -female,155.2 -female,162.8 -female,166.4 -female,157.4 -female,155.3 -female,150.9 -female,158.4 -female,155.4 -female,163.2 -female,168.3 -female,145.5 -female,154.6 -female,147.4 -female,158.8 -female,174.1 -female,153.9 -female,162.3 -female,170.8 -female,165.5 -female,155.3 -female,161.2 -female,146.9 -female,156.5 -female,173.8 -female,154.1 -female,162.1 -female,160.1 -female,150.0 -female,151.6 -female,159.7 -female,163.5 -female,167.9 -female,156.4 -female,165.1 -female,159.8 -female,155.9 -female,165.2 -female,154.2 -female,158.9 -female,164.6 -female,143.9 -female,168.1 -female,154.1 -female,166.3 -female,158.7 -female,160.5 -female,158.0 -female,157.7 -female,155.3 -female,138.3 -female,159.7 -female,158.9 -female,173.0 -female,166.8 -female,166.0 -female,160.6 -female,161.4 -female,176.5 -female,155.8 -female,156.1 -female,153.4 -female,148.8 -female,157.8 -female,161.2 -female,170.6 -female,159.9 -female,150.3 -female,163.0 -female,155.0 -female,151.6 -female,167.4 -female,152.7 -female,159.3 -female,157.9 -female,151.6 -female,165.0 -female,154.3 -female,150.1 -female,159.7 -female,151.2 -female,165.6 -female,161.3 -female,151.8 -female,151.0 -female,155.9 -female,176.6 -female,153.3 -female,153.5 -female,151.6 -female,160.8 -female,148.8 -female,163.5 -female,153.7 -female,167.8 -female,152.9 -female,167.5 -female,148.8 -female,153.5 -female,159.1 -female,166.8 -female,160.1 -female,164.1 -female,147.6 -female,163.7 -female,157.1 -female,161.7 -female,155.3 -female,161.1 -female,167.5 -female,151.4 -female,163.9 -female,166.0 -female,150.7 -female,159.4 -female,168.0 -female,161.4 -female,157.0 -female,151.0 -female,171.6 -female,152.5 -female,159.3 -female,157.3 -female,164.8 -female,150.7 -female,156.5 -female,163.2 -female,163.4 -female,157.5 -female,162.4 -female,159.2 -female,161.2 -female,160.7 -female,161.4 -female,168.7 -female,161.9 -female,166.1 -female,158.4 -female,167.6 -female,164.9 -female,177.7 -female,153.7 -female,165.1 -female,155.5 -female,163.6 -female,160.5 -female,163.8 -female,172.9 -female,160.6 -female,143.5 -female,165.1 -female,154.0 -female,164.0 -female,162.7 -female,157.5 -female,152.6 -female,154.5 -female,167.9 -female,178.4 -female,156.8 -female,167.5 -female,158.2 -female,160.1 -female,147.8 -female,166.0 -female,156.5 -female,152.6 -female,146.3 -female,162.6 -female,162.0 -female,157.0 -female,142.9 -female,155.2 -female,156.3 -female,170.9 -female,159.8 -female,157.0 -female,159.4 -female,163.6 -female,164.8 -female,161.6 -female,159.0 -female,171.4 -female,170.2 -female,152.6 -female,156.8 -female,170.4 -female,159.2 -female,163.2 -female,161.6 -female,150.9 -female,161.7 -female,161.2 -female,139.7 -female,155.1 -female,156.5 -female,165.9 -female,154.7 -female,154.7 -female,159.8 -female,158.8 -female,169.0 -female,153.6 -female,145.7 -female,163.6 -female,163.0 -female,145.6 -female,151.3 -female,149.2 -female,156.5 -female,161.8 -female,153.5 -female,159.8 -female,149.1 -female,157.4 -female,152.0 -female,163.2 -female,161.5 -female,168.2 -female,158.7 -female,161.4 -female,166.5 -female,147.0 -female,156.0 -female,160.8 -female,154.1 -female,157.4 -female,151.6 -female,155.6 -female,155.6 -female,151.2 -female,176.7 -female,155.1 -female,151.2 -female,148.9 -female,163.1 -female,156.2 -female,154.6 -female,159.3 -female,165.6 -female,154.5 -female,166.8 -female,163.1 -female,156.8 -female,154.6 -female,154.9 -female,172.4 -female,161.2 -female,147.5 -female,148.2 -female,166.1 -female,151.3 -female,163.4 -female,160.5 -female,156.2 -female,149.5 -female,151.1 -female,156.2 -female,159.9 -female,165.6 -female,154.2 -female,157.9 -female,164.9 -female,154.3 -female,175.8 -female,159.9 -female,152.4 -female,164.1 -female,153.1 -female,147.9 -female,162.1 -female,142.7 -female,167.8 -female,172.4 -female,156.1 -female,151.4 -female,162.4 -female,160.7 -female,160.7 -female,158.4 -female,165.3 -female,162.4 -female,164.2 -female,150.0 -female,160.6 -female,150.8 -female,154.9 -female,160.3 -female,154.3 -female,152.7 -female,156.1 -female,166.7 -female,164.4 -female,169.0 -female,154.8 -female,150.4 -female,157.0 -female,154.8 -female,158.9 -female,153.6 -female,168.0 -female,150.1 -female,158.6 -female,160.0 -female,159.1 -female,168.0 -female,154.0 -female,163.8 -female,166.8 -female,161.8 -female,159.2 -female,151.9 -female,154.8 -female,159.6 -female,162.3 -female,171.5 -female,163.0 -female,161.4 -female,165.8 -female,155.3 -female,161.8 -female,153.6 -female,151.4 -female,158.6 -female,155.8 -female,160.8 -female,157.4 -female,166.6 -female,172.9 -female,159.6 -female,173.4 -female,164.2 -female,163.9 -female,174.8 -female,167.0 -female,164.9 -female,163.4 -female,159.7 -female,162.8 -female,165.3 -female,163.6 -female,167.7 -female,156.7 -female,156.3 -female,156.3 -female,160.6 -female,165.9 -female,162.4 -female,160.7 -female,156.5 -female,169.7 -female,167.0 -female,163.2 -female,156.4 -female,177.1 -female,157.8 -female,151.5 -female,160.3 -female,160.9 -female,150.3 -female,146.1 -female,148.7 -female,163.2 -female,161.4 -female,174.7 -female,158.3 -female,158.7 -female,153.9 -female,159.8 -female,158.5 -female,163.1 -female,164.4 -female,151.1 -female,164.5 -female,163.3 -female,153.1 -female,159.6 -female,164.0 -female,165.3 -female,172.3 -female,168.1 -female,164.4 -female,163.0 -female,171.6 -female,161.1 -female,161.0 -female,159.7 -female,151.2 -female,162.2 -female,158.0 -female,163.3 -female,171.3 -female,172.5 -female,162.1 -female,158.1 -female,161.8 -female,164.6 -female,166.2 -female,146.7 -female,160.3 -female,152.5 -female,149.3 -female,159.5 -female,157.4 -female,156.5 -female,171.6 -female,151.5 -female,149.8 -female,155.1 -female,160.6 -female,156.6 -female,158.0 -female,159.2 -female,155.4 -female,160.2 -female,165.1 -female,153.5 -female,173.3 -female,163.5 -female,169.7 -female,156.8 -female,167.9 -female,157.7 -female,153.2 -female,168.7 -female,154.5 -female,157.1 -female,170.1 -female,153.4 -female,159.9 -female,161.3 -female,157.7 -female,157.7 -female,156.8 -female,155.6 -female,155.7 -female,171.4 -female,161.6 -female,155.1 -female,154.4 -female,160.6 -female,162.0 -female,164.1 -female,177.1 -female,163.8 -female,157.0 -female,160.9 -female,170.2 -female,155.0 -female,159.0 -female,162.5 -female,160.2 -female,150.7 -female,153.0 -female,163.9 -female,167.1 -female,150.9 -female,157.3 -female,174.8 -female,154.6 -female,161.3 -female,160.6 -female,155.1 -female,171.0 -female,157.1 -female,171.9 -female,160.3 -female,162.1 -female,159.2 -female,151.1 -female,149.5 -female,170.5 -female,167.8 -female,161.4 -female,159.9 -female,149.6 -female,165.5 -female,167.0 -female,156.9 -female,160.5 -female,172.5 -female,165.2 -female,156.4 -female,157.3 -female,152.2 -female,155.7 -female,163.7 -female,158.6 -female,168.8 -female,156.6 -female,163.1 -female,155.2 -female,150.7 -female,152.3 -female,149.9 -female,156.9 -female,163.0 -female,157.0 -female,153.9 -female,154.7 -female,157.4 -female,155.7 -female,162.3 -female,151.8 -female,150.7 -female,161.7 -female,156.3 -female,155.4 -female,157.3 -female,157.9 -female,155.5 -female,161.1 -female,168.1 -female,159.1 -female,148.7 -female,162.4 -female,155.3 -female,162.8 -female,152.4 -female,153.1 -female,164.0 -female,153.5 -female,156.3 -female,165.9 -female,172.6 -female,153.1 -female,156.1 -female,166.7 -female,161.7 -female,153.0 -female,151.5 -female,161.1 -female,161.8 -female,169.5 -female,151.5 -female,174.7 -female,149.3 -female,157.9 -female,156.2 -female,163.1 -female,156.3 -female,152.7 -female,170.7 -female,160.6 -female,156.2 -female,155.7 -female,163.8 -female,151.1 -female,164.3 -female,154.0 -female,168.4 -female,154.1 -female,162.0 -female,159.3 -female,158.9 -female,171.5 -female,160.7 -female,151.8 -female,157.4 -female,157.0 -female,155.3 -female,157.9 -female,161.9 -female,166.8 -female,162.7 -female,165.1 -female,161.2 -female,155.0 -female,154.9 -female,169.7 -female,171.1 -female,164.8 -female,161.5 -female,156.3 -female,154.5 -female,159.6 -female,160.7 -female,168.2 -female,156.4 -female,145.3 -female,163.0 -female,162.2 -female,154.5 -female,163.8 -female,154.9 -female,160.7 -female,166.1 -female,160.1 -female,163.2 -female,161.6 -female,173.8 -female,157.0 -female,166.1 -female,156.7 -female,154.1 -female,151.9 -female,163.5 -female,160.3 -female,156.9 -female,161.8 -female,146.8 -female,165.9 -female,158.8 -female,153.7 -female,169.6 -female,147.3 -female,166.7 -female,157.5 -female,163.4 -female,158.0 -female,156.3 -female,161.8 -female,173.8 -female,162.8 -female,152.3 -female,158.6 -female,157.9 -female,146.8 -female,149.7 -female,175.9 -female,163.5 -female,166.6 -female,151.6 -female,161.9 -female,164.1 -female,164.8 -female,157.0 -female,162.1 -female,158.6 -female,167.0 -female,150.4 -female,164.9 -female,155.0 -female,162.7 -female,156.2 -female,163.0 -female,155.0 -female,156.9 -female,169.3 -female,150.8 -female,170.2 -female,160.3 -female,146.9 -female,167.1 -female,165.9 -female,170.2 -female,168.3 -female,155.0 -female,161.4 -female,168.6 -female,160.1 -female,161.2 -female,152.7 -female,160.9 -female,153.9 -female,154.9 -female,165.0 -female,166.3 -female,167.7 -female,156.2 -female,161.7 -female,162.3 -female,169.0 -female,149.4 -female,158.7 -female,171.0 -female,163.8 -female,166.6 -female,161.4 -female,154.5 -female,165.0 -female,154.1 -female,162.6 -female,158.8 -female,165.5 -female,158.8 -female,158.9 -female,148.3 -female,162.3 -female,170.2 -female,148.4 -female,154.4 -female,147.9 -female,163.2 -female,166.7 -female,159.5 -female,161.4 -female,157.2 -female,161.1 -female,163.6 -female,161.7 -female,155.9 -female,151.0 -female,164.6 -female,160.5 -female,163.9 -female,158.6 -female,158.8 -female,153.9 -female,163.0 -female,160.4 -female,172.9 -female,161.8 -female,159.6 -female,153.0 -female,149.4 -female,165.0 -female,167.6 -female,169.1 -female,151.1 -female,152.1 -female,155.1 -female,141.9 -female,177.2 -female,159.2 -female,164.8 -female,165.6 -female,163.4 -female,143.3 -female,153.5 -female,157.3 -female,157.8 -female,152.9 -female,170.2 -female,166.3 -female,153.7 -female,155.5 -female,155.7 -female,155.9 -female,150.9 -female,168.3 -female,163.6 -female,155.6 -female,152.4 -female,160.9 -female,164.8 -female,159.4 -female,164.6 -female,157.6 -female,160.3 -female,167.3 -female,143.9 -female,175.0 -female,164.0 -female,161.2 -female,152.2 -female,155.7 -female,147.6 -female,152.4 -female,157.3 -female,149.1 -female,167.0 -female,159.1 -female,168.0 -female,152.5 -female,157.3 -female,140.8 -female,163.3 -female,155.8 -female,149.7 -female,165.5 -female,157.1 -female,172.6 -female,161.6 -female,154.4 -female,161.0 -female,149.5 -female,173.6 -female,152.7 -female,144.2 -female,149.0 -female,144.6 -female,165.1 -female,168.1 -female,162.0 -female,159.1 -female,165.0 -female,167.2 -female,157.0 -female,163.7 -female,155.7 -female,146.4 -female,166.5 -female,173.0 -female,149.9 -female,163.0 -female,165.3 -female,161.0 -female,163.3 -female,159.2 -female,161.4 -female,165.2 -female,170.8 -female,164.8 -female,171.0 -female,157.0 -female,158.8 -female,163.0 -female,163.2 -female,156.4 -female,163.2 -female,157.8 -female,171.8 -female,162.9 -female,164.5 -female,176.0 -female,163.8 -female,156.4 -female,153.6 -female,178.0 -female,151.8 -female,155.0 -female,166.4 -female,161.9 -female,163.3 -female,163.6 -female,167.3 -female,155.7 -female,165.7 -female,145.6 -female,157.4 -female,162.9 -female,150.0 -female,151.1 -female,163.6 -female,155.3 -female,159.0 -female,152.8 -female,171.2 -female,163.8 -female,164.2 -female,171.1 -female,156.8 -female,156.0 -female,157.9 -female,164.3 -female,157.7 -female,163.7 -female,164.1 -female,154.6 -female,161.8 -female,164.1 -female,164.8 -female,158.6 -female,163.0 -female,165.7 -female,162.4 -female,143.5 -female,157.9 -female,164.0 -female,159.2 -female,165.0 -female,166.0 -female,158.5 -female,147.6 -female,155.2 -female,160.4 -female,159.1 -female,180.6 -female,161.1 -female,161.1 -female,159.1 -female,149.9 -female,161.7 -female,152.4 -female,154.7 -female,149.6 -female,157.0 -female,160.2 -female,163.0 -female,164.7 -female,156.4 -female,157.9 -female,163.6 -female,159.3 -female,170.2 -female,161.0 -female,156.9 -female,168.3 -female,154.3 -female,174.5 -female,187.8 -female,156.0 -female,155.0 -female,162.9 -female,165.2 -female,149.5 -female,160.8 -female,157.7 -female,147.8 -female,159.0 -female,156.7 -female,159.4 -female,163.5 -female,169.2 -female,158.5 -female,170.7 -female,154.5 -female,150.5 -female,163.2 -female,163.3 -female,164.0 -female,159.6 -female,154.0 -female,152.2 -female,155.8 -female,168.5 -female,155.2 -female,155.6 -female,151.1 -female,154.7 -female,153.9 -female,170.8 -female,159.0 -female,159.0 -female,159.7 -female,159.2 -female,164.0 -female,157.0 -female,160.2 -female,168.4 -female,170.6 -female,161.3 -female,159.3 -female,152.9 -female,160.5 -female,166.3 -female,149.2 -female,166.7 -female,160.8 -female,143.8 -female,155.5 -female,172.5 -female,171.1 -female,156.3 -female,163.4 -female,158.7 -female,162.5 -female,167.1 -female,189.3 -female,162.1 -female,158.9 -female,169.1 -female,169.8 -female,167.7 -female,152.1 -female,152.8 -female,162.5 -female,150.1 -female,170.2 -female,154.6 -female,155.8 -female,162.5 -female,154.6 -female,160.9 -female,151.3 -female,163.3 -female,155.7 -female,145.4 -female,169.8 -female,162.9 -female,171.9 -female,147.3 -female,166.6 -female,149.9 -female,152.0 -female,159.3 -female,161.0 -female,169.2 -female,146.6 -female,160.4 -female,164.0 -female,166.4 -female,157.3 -female,156.9 -female,148.1 -female,157.9 -female,165.2 -female,158.8 -female,157.8 -female,166.1 -female,161.0 -female,164.0 -female,159.8 -female,167.5 -female,152.6 -female,156.7 -female,163.7 -female,145.5 -female,148.7 -female,146.0 -female,149.4 -female,161.4 -female,149.0 -female,154.1 -female,151.3 -female,159.8 -female,155.6 -female,166.3 -female,156.0 -female,152.2 -female,158.4 -female,165.1 -female,157.5 -female,154.2 -female,172.2 -female,158.0 -female,159.2 -female,168.1 -female,165.5 -female,147.9 -female,161.0 -female,168.4 -female,166.7 -female,159.5 -female,161.0 -female,155.2 -female,165.0 -female,160.9 -female,144.9 -female,146.1 -female,156.2 -female,144.8 -female,162.2 -female,153.5 -female,166.6 -female,158.2 -female,152.9 -female,169.1 -female,156.3 -female,147.2 -female,166.9 -female,164.6 -female,146.6 -female,166.3 -female,160.8 -female,155.9 -female,158.1 -female,148.6 -female,151.6 -female,165.2 -female,164.9 -female,155.9 -female,162.2 -female,162.2 -female,165.3 -female,154.9 -female,154.2 -female,165.9 -female,160.4 -female,152.7 -female,160.5 -female,147.4 -female,158.0 -female,167.7 -female,154.5 -female,155.8 -female,150.5 -female,154.5 -female,154.7 -female,162.5 -female,159.8 -female,145.6 -female,150.2 -female,160.0 -female,162.5 -female,154.0 -female,161.8 -female,157.8 -female,164.5 -female,160.4 -female,154.6 -female,150.3 -female,153.9 -female,166.7 -female,160.4 -female,155.0 -female,156.7 -female,155.0 -female,153.2 -female,159.2 -female,156.0 -female,147.8 -female,162.3 -female,152.9 -female,162.9 -female,150.7 -female,162.9 -female,158.3 -female,152.7 -female,160.1 -female,162.8 -female,155.4 -female,159.3 -female,164.1 -female,161.1 -female,143.9 -female,160.1 -female,173.6 -female,160.1 -female,155.1 -female,153.7 -female,148.1 -female,162.6 -female,161.5 -female,160.9 -female,155.9 -female,161.5 -female,168.5 -female,155.5 -female,153.2 -female,159.4 -female,174.9 -female,170.8 -female,147.6 -female,158.2 -female,152.4 -female,164.9 -female,162.3 -female,169.1 -female,159.7 -female,166.7 -female,163.3 -female,159.7 -female,152.0 -female,176.9 -female,168.3 -female,155.1 -female,161.6 -female,157.6 -female,156.5 -female,155.0 -female,165.6 -female,162.8 -female,150.0 -female,170.2 -female,173.5 -female,151.0 -female,153.8 -female,158.4 -female,155.3 -female,157.4 -female,159.1 -female,167.4 -female,162.2 -female,159.7 -female,162.1 -female,159.1 -female,149.3 -female,146.4 -female,163.1 -female,178.8 -female,146.2 -female,155.0 -female,161.8 -female,157.2 -female,155.8 -female,151.1 -female,170.9 -female,154.9 -female,162.3 -female,170.4 -female,169.9 -female,149.4 -female,159.3 -female,152.8 -female,171.8 -female,161.6 -female,161.6 -female,164.9 -female,160.2 -female,171.8 -female,153.2 -female,162.1 -female,159.8 -female,156.7 -female,155.6 -female,172.2 -female,157.5 -female,158.8 -female,155.8 -female,155.1 -female,166.1 -female,158.7 -female,164.2 -female,180.4 -female,153.0 -female,155.5 -female,152.2 -female,160.6 -female,168.0 -female,165.3 -female,162.2 -female,152.5 -female,157.1 -female,151.4 -female,151.4 -female,151.5 -female,158.0 -female,158.3 -female,164.9 -female,152.0 -female,157.6 -female,151.3 -female,154.1 -female,159.6 -female,147.0 -female,144.1 -female,166.0 -female,161.7 -female,163.5 -female,155.7 -female,159.1 -female,165.5 -female,163.3 -female,160.7 -female,157.8 -female,160.5 -female,157.7 -female,162.8 -female,174.0 -female,154.8 -female,167.3 -female,150.7 -female,172.3 -female,148.0 -female,176.6 -female,164.0 -female,160.3 -female,158.8 -female,170.5 -female,154.6 -female,160.0 -female,166.4 -female,161.0 -female,163.2 -female,153.7 -female,164.3 -female,153.3 -female,145.1 -female,158.7 -female,149.8 -female,163.4 -female,152.8 -female,165.3 -female,166.2 -female,165.1 -female,152.4 -female,159.0 -female,170.9 -female,150.4 -female,163.8 -female,153.3 -female,164.6 -female,168.3 -female,153.3 -female,161.6 -female,159.0 -female,165.8 -female,177.7 -female,164.1 -female,170.7 -female,158.1 -female,161.6 -female,159.0 -female,159.2 -female,149.5 -female,159.1 -female,156.4 -female,157.1 -female,160.4 -female,157.0 -female,160.6 -female,158.5 -female,155.4 -female,165.6 -female,170.2 -female,152.3 -female,161.6 -female,160.5 -female,160.2 -female,158.2 -female,153.4 -female,163.9 -female,156.2 -female,154.6 -female,157.9 -female,164.0 -female,167.4 -female,153.5 -female,163.8 -female,158.3 -female,150.6 -female,171.6 -female,164.9 -female,165.5 -female,166.1 -female,168.8 -female,149.5 -female,164.2 -female,149.2 -female,156.0 -female,159.2 -female,179.8 -female,156.5 -female,153.6 -female,170.1 -female,167.4 -female,161.0 -female,154.8 -female,152.5 -female,159.4 -female,159.1 -female,148.8 -female,153.1 -female,162.1 -female,147.3 -female,164.8 -female,154.5 -female,146.7 -female,162.2 -female,155.2 -female,151.5 -female,152.0 -female,157.8 -female,154.5 -female,153.8 -female,154.8 -female,167.6 -female,156.8 -female,173.8 -female,155.7 -female,159.6 -female,154.1 -female,154.9 -female,162.5 -female,158.3 -female,152.0 -female,156.9 -female,159.5 -female,170.6 -female,158.2 -female,153.3 -female,157.6 -female,150.6 -female,144.8 -female,166.8 -female,158.2 -female,162.1 -female,155.8 -female,158.1 -female,153.2 -female,168.7 -female,161.8 -female,159.2 -female,170.2 -female,162.7 -female,156.4 -female,173.6 -female,158.6 -female,163.3 -female,152.9 -female,158.0 -female,173.5 -female,163.4 -female,148.6 -female,144.5 -female,154.2 -female,165.0 -female,151.2 -female,161.4 -female,155.7 -female,155.6 -female,159.2 -female,172.5 -female,171.9 -female,169.7 -female,162.5 -female,156.3 -female,160.2 -female,164.6 -female,154.4 -female,163.3 -female,159.8 -female,156.8 -female,167.3 -female,161.2 -female,152.9 -female,149.4 -female,170.1 -female,162.1 -female,164.3 -female,155.0 -female,161.2 -female,166.9 -female,168.8 -female,165.7 -female,164.4 -female,161.8 -female,169.5 -female,165.3 -female,154.1 -female,161.8 -female,153.7 -female,158.3 -female,148.4 -female,156.1 -female,173.7 -female,152.5 -female,165.6 -female,157.5 -female,156.9 -female,147.2 -female,148.1 -female,150.5 -female,159.2 -female,165.9 -female,154.9 -female,153.8 -female,156.4 -female,155.0 -female,153.5 -female,165.5 -female,159.5 -female,159.4 -female,159.4 -female,160.9 -female,149.8 -female,163.3 -female,152.5 -female,149.7 -female,159.7 -female,154.3 -female,165.2 -female,158.2 -female,155.9 -female,154.4 -female,157.7 -female,153.3 -female,158.9 -female,162.0 -female,158.9 -female,163.9 -female,157.0 -female,155.8 -female,155.0 -female,168.0 -female,148.7 -female,158.2 -female,153.3 -female,158.5 -female,153.5 -female,170.9 -female,167.4 -female,162.8 -female,147.0 -female,156.5 -female,152.3 -female,155.5 -female,170.6 -female,182.4 -female,151.1 -female,162.0 -female,162.9 -female,162.1 -female,166.8 -female,152.9 -female,156.9 -female,152.2 -female,162.2 -female,151.7 -female,145.7 -female,153.2 -female,167.9 -female,170.6 -female,171.3 -female,149.9 -female,147.1 -female,173.0 -female,160.5 -female,161.2 -female,164.9 -female,155.0 -female,165.3 -female,156.9 -female,150.5 -female,156.7 -female,167.5 -female,160.6 -female,152.5 -female,163.7 -female,163.7 -female,163.4 -female,161.9 -female,168.8 -female,159.2 -female,164.6 -female,171.0 -female,163.3 -female,161.2 -female,168.5 -female,152.1 -female,158.9 -female,152.4 -female,166.3 -female,157.9 -female,160.8 -female,152.0 -female,158.5 -female,167.4 -female,158.2 -female,167.1 -female,171.3 -female,157.3 -female,154.6 -female,161.3 -female,162.6 -female,166.0 -female,156.7 -female,169.8 -female,156.3 -female,146.7 -female,156.5 -female,160.1 -female,146.7 -female,170.8 -female,160.4 -female,152.5 -female,160.8 -female,177.8 -female,167.0 -female,153.9 -female,148.5 -female,162.5 -female,160.9 -female,156.9 -female,153.9 -female,157.9 -female,167.1 -female,157.4 -female,169.7 -female,155.6 -female,155.4 -female,156.9 -female,158.6 -female,166.4 -female,157.4 -female,156.9 -female,160.8 -female,156.6 -female,154.8 -female,157.9 -female,161.0 -female,161.5 -female,168.3 -female,168.4 -female,172.8 -female,162.6 -female,160.3 -female,163.8 -female,164.1 -female,154.0 -female,158.4 -female,163.2 -female,166.0 -female,163.8 -female,171.4 -female,169.3 -female,159.2 -female,156.2 -female,158.2 -female,152.3 -female,166.2 -female,142.3 -female,163.1 -female,154.5 -female,163.1 -female,155.6 -female,161.9 -female,166.4 -female,162.3 -female,152.3 -female,159.1 -female,172.3 -female,166.7 -female,170.0 -female,156.5 -female,166.9 -female,157.9 -female,159.1 -female,165.1 -female,150.1 -female,163.4 -female,155.1 -female,150.8 -female,167.2 -female,172.6 -female,154.8 -female,166.4 -female,158.6 -female,155.0 -female,171.4 -female,159.7 -female,165.2 -female,161.8 -female,164.5 -female,162.9 -female,156.0 -female,155.3 -female,159.8 -female,157.9 -female,166.3 -female,158.0 -female,151.9 -female,159.7 -female,158.4 -female,168.1 -female,149.2 -female,149.5 -female,168.4 -female,155.7 -female,161.4 -female,171.4 -female,163.6 -female,156.5 -female,151.6 -female,158.8 -female,151.4 -female,155.0 -female,158.8 -female,164.7 -female,157.6 -female,159.5 -female,155.3 -female,154.8 -female,151.1 -female,168.7 -female,156.7 -female,153.2 -female,156.7 -female,158.5 -female,168.3 -female,169.1 -female,157.0 -female,153.4 -female,148.3 -female,154.7 -female,156.6 -female,164.6 -female,155.7 -female,159.4 -female,151.6 -female,159.0 -female,156.4 -female,153.8 -female,158.4 -female,171.1 -female,157.0 -female,163.5 -female,157.9 -female,161.9 -female,154.4 -female,161.7 -female,152.9 -female,170.1 -female,150.3 -female,158.8 -female,165.1 -female,161.4 -female,162.6 -female,157.4 -female,161.6 -female,159.6 -female,163.9 -female,170.3 -female,171.4 -female,165.7 -female,162.2 -female,174.1 -female,166.0 -female,164.5 -female,157.0 -female,160.6 -female,167.7 -female,169.0 -female,145.9 -female,161.4 -female,157.1 -female,165.6 -female,160.2 -female,155.5 -female,165.6 -female,163.8 -female,165.5 -female,165.0 -female,156.3 -female,160.1 -female,163.8 -female,164.0 -female,161.8 -female,150.9 -female,152.4 -female,151.6 -female,161.8 -female,143.9 -female,158.1 -female,155.0 -female,164.9 -female,155.5 -female,162.1 -female,160.2 -female,139.0 -female,168.0 -female,169.0 -female,162.0 -female,161.6 -female,154.5 -female,154.9 -female,162.2 -female,160.7 -female,173.6 -female,175.7 -female,162.3 -female,146.3 -female,154.5 -female,144.2 -female,160.8 -female,149.9 -female,156.0 -female,177.2 -female,150.7 -female,165.3 -female,158.5 -female,149.7 -female,155.7 -female,160.3 -female,146.5 -female,155.3 -female,157.3 -female,170.5 -female,156.6 -female,160.6 -female,140.5 -female,166.8 -female,162.3 -female,153.0 -female,162.5 -female,160.2 -female,163.2 -female,159.1 -female,155.5 -female,151.1 -female,159.5 -female,158.6 -female,154.6 -female,166.8 -female,156.9 -female,160.2 -female,158.7 -female,147.5 -female,163.0 -female,150.3 -female,143.1 -female,160.8 -female,163.1 -female,152.8 -female,142.6 -female,157.5 -female,151.4 -female,171.8 -female,164.2 -female,161.3 -female,167.6 -female,155.7 -female,166.0 -female,152.6 -female,166.3 -female,158.9 -female,153.5 -female,157.7 -female,164.3 -female,151.7 -female,157.1 -female,149.5 -female,155.0 -female,158.1 -female,161.1 -female,174.9 -female,157.5 -female,171.5 -female,154.9 -female,157.2 -female,160.4 -female,156.5 -female,151.0 -female,168.0 -female,155.5 -female,156.1 -female,155.4 -female,154.5 -female,153.7 -female,152.3 -female,158.1 -female,168.3 -female,152.8 -female,160.4 -female,161.1 -female,151.4 -female,141.7 -female,158.1 -female,145.8 -female,159.7 -female,155.7 -female,168.7 -female,153.3 -female,163.5 -female,159.4 -female,153.8 -female,168.7 -female,171.0 -female,139.7 -female,166.4 -female,162.6 -female,152.7 -female,159.6 -female,164.9 -female,167.6 -female,161.9 -female,152.4 -female,157.2 -female,157.0 -female,160.8 -female,150.6 -female,154.2 -female,165.3 -female,160.0 -female,160.5 -female,166.4 -female,154.4 -female,160.8 -female,151.5 -female,180.0 -female,149.2 -female,162.4 -female,163.6 -female,153.3 -female,151.5 -female,157.2 -female,168.0 -female,162.0 -female,172.5 -female,168.3 -female,145.9 -female,161.2 -female,163.1 -female,155.9 -female,160.5 -female,155.3 -female,174.6 -female,153.9 -female,161.5 -female,164.1 -female,167.9 -female,154.2 -female,161.8 -female,149.2 -female,158.6 -female,150.0 -female,164.8 -female,162.6 -female,148.4 -female,161.5 -female,170.7 -female,166.8 -female,168.9 -female,144.9 -female,159.8 -female,151.6 -female,160.8 -female,160.0 -female,152.2 -female,176.4 -female,158.2 -female,159.4 -female,177.5 -female,170.0 -female,157.8 -female,153.5 -female,159.3 -female,164.1 -female,150.7 -female,149.1 -female,163.0 -female,158.8 -female,155.2 -female,154.1 -female,156.3 -female,149.0 -female,156.7 -female,154.4 -female,160.3 -female,147.3 -female,155.7 -female,165.9 -female,155.0 -female,163.2 -female,159.9 -female,165.8 -female,161.5 -female,160.3 -female,163.5 -female,158.4 -female,182.4 -female,157.0 -female,164.2 -female,161.7 -female,158.3 -female,158.0 -female,161.4 -female,157.8 -female,156.0 -female,150.6 -female,157.8 -female,164.9 -female,165.3 -female,154.4 -female,172.3 -female,159.7 -female,162.3 -female,155.3 -female,158.4 -female,155.4 -female,172.4 -female,164.2 -female,170.9 -female,159.0 -female,157.7 -female,165.7 -female,158.0 -female,162.0 -female,159.7 -female,154.7 -female,155.7 -female,165.2 -female,152.2 -female,154.1 -female,163.4 -female,161.7 -female,152.9 -female,149.9 -female,169.6 -female,163.4 -female,168.7 -female,151.9 -female,158.5 -female,163.5 -female,161.5 -female,157.3 -female,153.8 -female,146.0 -female,177.2 -female,151.1 -female,160.9 -female,165.5 -female,167.3 -female,150.6 -female,165.2 -female,169.5 -female,158.8 -female,148.5 -female,159.6 -female,151.8 -female,160.4 -female,170.6 -female,149.6 -female,163.0 -female,147.9 -female,155.4 -female,141.5 -female,164.1 -female,150.4 -female,153.8 -female,163.7 -female,152.8 -female,171.0 -female,162.7 -female,153.2 -female,160.2 -female,153.4 -female,157.2 -female,158.0 -female,163.9 -female,163.1 -female,165.3 -female,161.1 -female,154.2 -female,153.3 -female,153.5 -female,163.8 -female,152.0 -female,167.4 -female,156.6 -female,168.9 -female,148.8 -female,162.4 -female,149.3 -female,154.0 -female,156.7 -female,164.9 -female,156.5 -female,149.5 -female,156.2 -female,158.3 -female,167.2 -female,174.1 -female,146.1 -female,152.7 -female,162.7 -female,148.3 -female,164.7 -female,168.4 -female,157.5 -female,161.1 -female,153.5 -female,157.4 -female,173.2 -female,154.5 -female,153.8 -female,161.1 -female,158.2 -female,167.3 -female,155.6 -female,159.5 -female,157.9 -female,152.8 -female,156.6 -female,162.4 -female,161.0 -female,152.7 -female,164.4 -female,168.7 -female,164.4 -female,154.9 -female,154.7 -female,156.8 -female,162.6 -female,161.4 -female,151.5 -female,161.4 -female,153.1 -female,159.5 -female,172.6 -female,158.5 -female,150.8 -female,167.6 -female,169.4 -female,156.3 -female,166.6 -female,163.4 -female,157.3 -female,171.0 -female,157.1 -female,154.9 -female,162.5 -female,160.3 -female,169.0 -female,166.7 -female,155.4 -female,178.9 -female,150.8 -female,160.6 -female,169.8 -female,156.0 -female,161.3 -female,156.8 -female,159.1 -female,155.8 -female,160.6 -female,155.1 -female,164.8 -female,151.1 -female,154.2 -female,164.4 -female,152.3 -female,164.6 -female,167.0 -female,178.0 -female,160.3 -female,149.1 -female,152.5 -female,145.1 -female,156.8 -female,161.0 -female,155.6 -female,164.6 -female,145.9 -female,175.0 -female,164.6 -female,154.1 -female,159.2 -female,151.2 -female,169.6 -female,152.4 -female,167.8 -female,155.5 -female,159.1 -female,164.8 -female,164.6 -female,171.9 -female,162.1 -female,153.7 -female,162.0 -female,169.8 -female,156.9 -female,149.1 -female,167.8 -female,159.6 -female,173.9 -female,172.0 -female,167.9 -female,158.9 -female,181.1 -female,162.0 -female,156.5 -female,162.6 diff --git a/lectures/_static/quant-econ.bib b/lectures/_static/quant-econ.bib index 87f9d61d..4b35c494 100644 --- a/lectures/_static/quant-econ.bib +++ b/lectures/_static/quant-econ.bib @@ -2968,3 +2968,12 @@ @article{ricard2012 year={2012}, publisher={Wiley} } + +@article{decock2011ames, + title={Ames, Iowa: Alternative to the Boston housing data as an end of semester regression project}, + author={De Cock, Dean}, + journal={Journal of Statistics Education}, + volume={19}, + number={3}, + year={2011} +} diff --git a/lectures/_toc.yml b/lectures/_toc.yml index eb17a896..66c233c6 100644 --- a/lectures/_toc.yml +++ b/lectures/_toc.yml @@ -38,6 +38,7 @@ parts: numbered: true chapters: - file: prob_dist + - file: observed_distributions - file: lln_clt - file: monte_carlo - file: heavy_tails diff --git a/lectures/lln_clt.md b/lectures/lln_clt.md index 81b68a55..4b6425cf 100644 --- a/lectures/lln_clt.md +++ b/lectures/lln_clt.md @@ -295,7 +295,7 @@ as expected. Let's vary `n` to see how the distribution of the sample mean changes. -We will use a [violin plot](https://intro.quantecon.org/prob_dist.html#violin-plots) to show the different distributions. +We will use a {ref}`violin plot ` to show the different distributions. Each distribution in the violin plot represents the distribution of $X_n$ for some $n$, calculated by simulation. diff --git a/lectures/observed_distributions.md b/lectures/observed_distributions.md new file mode 100644 index 00000000..dada86ae --- /dev/null +++ b/lectures/observed_distributions.md @@ -0,0 +1,707 @@ +--- +jupytext: + text_representation: + extension: .md + format_name: myst + format_version: 0.13 + jupytext_version: 1.16.6 +kernelspec: + display_name: Python 3 (ipykernel) + language: python + name: python3 +--- + +(observed_distributions)= +# Observed Distributions + +```{index} single: Observed Distributions +``` + +## Outline + +In the lecture on {doc}`probability distributions ` we studied +probability distributions, which are mathematical objects. + +In this lecture we turn to observed data --- sets of numbers that we measure or +collect. + +We discuss how to summarize and visualize such data, and how observed data +connects back to probability distributions. + +```{code-cell} ipython3 +:tags: [hide-output] + +!pip install --upgrade yfinance +``` + +```{code-cell} ipython3 +import matplotlib.pyplot as plt +import pandas as pd +import numpy as np +import yfinance as yf +import scipy.stats +import seaborn as sns +``` + +Sometimes we refer to observed data or measurements as "distributions". + +For example, let's say we observe the income of 10 people over a year: + +```{code-cell} ipython3 +data = [['Hiroshi', 1200], + ['Ako', 1210], + ['Emi', 1400], + ['Daiki', 990], + ['Chiyo', 1530], + ['Taka', 1210], + ['Katsuhiko', 1240], + ['Daisuke', 1124], + ['Yoshi', 1330], + ['Rie', 1340]] + +df = pd.DataFrame(data, columns=['name', 'income']) +df +``` + +In this situation, we might refer to the set of their incomes as the "income distribution." + +The terminology is confusing because this set is not a probability distribution +--- it's just a collection of numbers. + +However, as we will see, there are connections between observed distributions (i.e., sets of +numbers like the income distribution above) and probability distributions. + +Below we explore some observed distributions. + + +## Sample moments + +Suppose we have an observed distribution with values $\{x_1, \ldots, x_n\}$ + +The **sample mean** of this distribution is defined as + +$$ +\bar x = \frac{1}{n} \sum_{i=1}^n x_i +$$ + +The **sample variance** is defined as + +$$ +s^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \bar x)^2 +$$ + +and the **sample standard deviation** $s$ is its square root. + +For the income distribution given above, we can calculate these numbers via + +```{code-cell} ipython3 +x = df['income'] +x.mean(), x.var(), x.std() +``` + +Each of these statistics is the sample counterpart of one of the population +quantities defined in {doc}`prob_dist`: we replace the probability distribution +by the observed data, weighting each observation equally. + +The same idea extends to higher moments. + +The **sample skewness** and **sample excess kurtosis** are + +$$ +\hat S = \frac{1}{n} \sum_{i=1}^n \left( \frac{x_i - \bar x}{s} \right)^3 +\qquad \text{and} \qquad +\hat K = \frac{1}{n} \sum_{i=1}^n \left( \frac{x_i - \bar x}{s} \right)^4 - 3 +$$ + +Recall from {doc}`prob_dist` that a normal distribution has both skewness and +excess kurtosis equal to zero. + +This gives us a first, purely numerical, way to ask whether a data set looks +normal. + +Let's try it on the heights of US adult women, which we saw were well described +by a normal distribution. + +```{code-cell} ipython3 +url = ('https://github.com/QuantEcon/data-lectures/raw/main/' + 'lectures/us_adult_heights.csv') +heights = pd.read_csv(url) +female = heights[heights['sex'] == 'female']['height_cm'] + +scipy.stats.skew(female), scipy.stats.kurtosis(female) +``` + +Both numbers are close to zero, which is consistent with what we saw in the +figures. + +Now let's look at a data set that is far from normal. + +The next cell reads in the sale prices of 2,930 houses sold in Ames, Iowa +between 2006 and 2010, along with a few characteristics of each house +{cite}`decock2011ames`. + +```{code-cell} ipython3 +url = ('https://github.com/QuantEcon/data-lectures/raw/main/' + 'lectures/ames_house_prices.csv') +houses = pd.read_csv(url) +houses.head() +``` + +Let's compute the same statistics for the sale prices. + +```{code-cell} ipython3 +price = houses['price'] +scipy.stats.skew(price), scipy.stats.kurtosis(price) +``` + +The skewness is large and positive, telling us that the data has a long right +tail --- a small number of houses sell for far more than the typical price. + +The excess kurtosis is also large, telling us that extreme values are much more +common than they would be for a normal distribution. + +We saw exactly this combination in {doc}`prob_dist` when we looked at the +lognormal distribution. + +That suggests taking logarithms. + +```{code-cell} ipython3 +log_price = np.log(price) +scipy.stats.skew(log_price), scipy.stats.kurtosis(log_price) +``` + +The skewness is now almost exactly zero. + +In other words, the *logarithm* of the sale price looks far more normal than the +sale price itself, which is the defining property of the lognormal distribution. + +Our last example runs in the opposite direction. + +The next cell reads the number of deaths in Japan in 2023 at each single year of +age, from the [World Population +Prospects](https://population.un.org/wpp/) of the United Nations. + +```{code-cell} ipython3 +url = ('https://github.com/QuantEcon/data-lectures/raw/main/' + 'lectures/japan_deaths_by_age.csv') +deaths = pd.read_csv(url) +deaths.tail() +``` + +The data arrive as counts, so we expand them into a data set with one +observation per death. + +```{code-cell} ipython3 +age_at_death = np.repeat(deaths['age'], deaths['deaths_total']) +len(age_at_death) +``` + +```{code-cell} ipython3 +scipy.stats.skew(age_at_death), scipy.stats.kurtosis(age_at_death) +``` + +Now the skewness is large and *negative*. + +Deaths cluster at high ages, with a long tail running down towards zero --- the +mirror image of the house price data. + +```{note} +The last age is recorded as "100 and over", so every death above age 100 is +counted as 100. + +This is not a negligible group in Japan: it accounts for 3.3% of all deaths and +5.7% of female deaths. + +We will see it below as a spike at the right-hand end of the histograms, which +is an artifact of how the data are recorded rather than a feature of the data. +``` + +```{exercise} +:label: obs_ex1 + +If you try to check that the formulas given above for the sample mean and sample +variance produce the same numbers, you will see that the variance isn't quite +right. This is because Pandas uses $1/(n-1)$ instead of $1/n$ as the term at the +front of the variance. (Some books define the sample variance this way.) +Confirm. +``` + +```{note} +The same issue arises with skewness and kurtosis, where different conventions +adjust the estimates in different ways. + +The Pandas methods `x.skew()` and `x.kurt()` apply such adjustments, so they do +not agree exactly with the formulas above, while `scipy.stats.skew` and +`scipy.stats.kurtosis` use the plain $1/n$ versions by default. + +The differences are small when $n$ is large. +``` + + +## Sample quantiles + +Not every useful summary statistic is a moment. + +If we sort the observations from smallest to largest, then the **sample +$\tau$-quantile** is the value below which a fraction $\tau$ of the +observations fall. + +The 0.5 quantile is the **sample median** and the 0.25 and 0.75 quantiles are +the first and third **sample quartiles**. + +Here are these values for the income data: + +```{code-cell} ipython3 +x.median(), x.quantile(0.25), x.quantile(0.75) +``` + +Sample quantiles are useful because they are barely affected by a small number +of extreme observations. + +To see this, let's replace the largest income in our data set with a very large +value and recompute the mean and the median. + +```{code-cell} ipython3 +x_outlier = x.copy() +x_outlier.iloc[x.argmax()] = 10_000_000 + +x.mean(), x_outlier.mean() +``` + +```{code-cell} ipython3 +x.median(), x_outlier.median() +``` + +The mean shifts enormously while the median does not move at all. + +The same issue arises with real data whenever the distribution is skewed. + +Here are the mean and the median sale price of houses in Ames: + +```{code-cell} ipython3 +price.mean(), price.median() +``` + +The mean exceeds the median by around 13%, pulled up by the expensive houses in +the right tail. + +This is why house prices are almost always reported as medians. + +For the age at death data the inequality runs the other way. + +```{code-cell} ipython3 +age_at_death.mean(), age_at_death.median() +``` + +Here the mean is pulled *below* the median, by deaths at young ages. + +In general, the mean sits on the side of the median towards which the data are +skewed. + +We will return to this point in {doc}`heavy_tails`. + + +## Visualization + +Summary statistics compress a data set down to a few numbers. + +Visualization goes the other way, showing us the whole shape of the data. + +We will cover + +- histograms +- empirical distribution functions +- kernel density estimates +- box-and-whisker plots and +- violin plots + + +### Histograms + +We can histogram the income distribution we just constructed as follows + +```{code-cell} ipython3 +fig, ax = plt.subplots() +ax.hist(x, bins=5, density=True, histtype='bar') +ax.set_xlabel('income') +ax.set_ylabel('density') +plt.show() +``` + +Here is a histogram of the Ames house prices. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +ax.hist(price, bins=50, density=True) +ax.set_xlabel('sale price (US$)') +ax.set_ylabel('density') +plt.show() +``` + +The long right tail that the skewness told us about is clearly visible. + +Let's compare this with the histogram of the log prices. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +ax.hist(log_price, bins=50, density=True) +ax.set_xlabel('log of sale price') +ax.set_ylabel('density') +plt.show() +``` + +The second histogram is far more symmetric, as the sample skewness led us to expect. + +Here is the age at death data, which we found to have negative skewness. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +ax.hist(age_at_death, bins=101, density=True) +ax.set_xlabel('age at death') +ax.set_ylabel('density') +plt.show() +``` + +The long tail now runs to the left, towards zero. + +Let's also compare men and women, using the sex-specific counts in the data +set. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +for sex in ('male', 'female'): + ax.hist(deaths['age'], weights=deaths[f'deaths_{sex}'], + bins=101, density=True, alpha=0.6, label=sex) +ax.set_xlabel('age at death') +ax.set_ylabel('density') +ax.legend() +plt.show() +``` + +The two distributions have a similar shape but the female distribution sits to +the right of the male distribution. + +The median age at death is 82 for men and 88 for women. + +The spike at the right-hand end is the "100 and over" category discussed above, +which is far larger for women. + +(Notice that we did not need to expand the counts here, since `hist` accepts +the counts directly as weights.) + +Let's look at another distribution from real data. + +In particular, we will look at the monthly return on Amazon shares between 2000/1/1 and 2024/1/1. + +The monthly return is calculated as the percent change in the share price over each month. + +So we will have one observation for each month. + +```{code-cell} ipython3 +:tags: [hide-output] + +df = yf.download('AMZN', '2000-1-1', '2024-1-1', interval='1mo') +prices = df['Close'] +x_amazon = prices.pct_change()[1:] * 100 +x_amazon.head() +``` + +The first observation is the monthly return (percent change) over January 2000, which was + +```{code-cell} ipython3 +x_amazon.iloc[0] +``` + +Let's turn the return observations into an array and histogram it. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +ax.hist(x_amazon, bins=20) +ax.set_xlabel('monthly return (percent change)') +ax.set_ylabel('density') +plt.show() +``` + +### Empirical distribution functions + +A histogram estimates the density of the data. + +The **empirical distribution function** (EDF), also called the empirical CDF, +does the same job for the CDF. + +For a sample $\{x_1, \ldots, x_n\}$ it is defined as + +$$ +F_n(x) = \frac{1}{n} \sum_{i=1}^n \mathbb 1 \{x_i \leq x\} +$$ + +In words, $F_n(x)$ is just the fraction of observations that are less than or +equal to $x$. + +The EDF is a step function that jumps up by $1/n$ at each observation. + +Here is a function that plots it, obtained by sorting the data and stepping up +as we move from left to right. + +```{code-cell} ipython3 +def plot_edf(sample, ax, **kwargs): + x_sorted = np.sort(sample) + n = len(x_sorted) + ax.step(x_sorted, np.arange(1, n+1) / n, where='post', **kwargs) +``` + +Let's apply it to the house price data. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +plot_edf(price, ax) +ax.set_xlabel('sale price (US$)') +ax.set_ylabel('EDF') +plt.show() +``` + +Unlike a histogram, the EDF requires no choice of bin width --- it uses the data +exactly as they are. + +This makes it a good tool for comparing a data set with a probability +distribution, since we can simply plot the two curves on the same axes. + +Let's compare the log prices with the CDF of the normal distribution that has +the same mean and standard deviation. + +```{code-cell} ipython3 +u = scipy.stats.norm(log_price.mean(), log_price.std()) +x_grid = np.linspace(log_price.min(), log_price.max(), 200) + +fig, ax = plt.subplots() +plot_edf(log_price, ax, label='EDF of log prices') +ax.plot(x_grid, u.cdf(x_grid), 'k--', alpha=0.7, label='normal CDF') +ax.set_xlabel('log of sale price') +ax.set_ylabel('probability') +ax.legend() +plt.show() +``` + +The two curves are close, although the fit is not perfect in the tails. + +(Seaborn provides `sns.ecdfplot`, which produces the same figure with less code.) + + +### Kernel density estimates + +Kernel density estimates (KDE) provide a simple way to estimate and visualize the density of a distribution. + +If you are not familiar with KDEs, you can think of them as a smoothed +histogram. + +Let's have a look at a KDE formed from the Amazon return data. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +sns.kdeplot(x_amazon, ax=ax) +ax.set_xlabel('monthly return (percent change)') +ax.set_ylabel('KDE') +plt.show() +``` + +The smoothness of the KDE is dependent on how we choose the bandwidth. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +sns.kdeplot(x_amazon, ax=ax, bw_adjust=0.1, alpha=0.5, label="bw=0.1") +sns.kdeplot(x_amazon, ax=ax, bw_adjust=0.5, alpha=0.5, label="bw=0.5") +sns.kdeplot(x_amazon, ax=ax, bw_adjust=1, alpha=0.5, label="bw=1") +ax.set_xlabel('monthly return (percent change)') +ax.set_ylabel('KDE') +plt.legend() +plt.show() +``` + +When we use a larger bandwidth, the KDE is smoother. + +A suitable bandwidth is not too smooth (underfitting) or too wiggly (overfitting). + + +### Box-and-whisker plots + +A box-and-whisker plot (or box plot) summarizes a distribution using the sample +quantiles discussed above. + +The box spans the first and third quartiles, so its width is the interquartile +range, and the line inside it is the median. + +The whiskers extend to the most extreme observations lying within 1.5 +interquartile ranges of the box, and observations beyond them are plotted +individually. + +Box plots discard a lot of information, which makes them well suited to +comparing many groups at once. + +For example, let's compare house prices across houses with different numbers of +bedrooms. + +```{code-cell} ipython3 +bedroom_counts = (1, 2, 3, 4, 5) +groups = [price[houses['bedrooms'] == b] for b in bedroom_counts] + +fig, ax = plt.subplots() +ax.boxplot(groups, tick_labels=bedroom_counts) +ax.set_xlabel('bedrooms') +ax.set_ylabel('sale price (US$)') +plt.show() +``` + +The figure carries a warning about reading too much into group averages. + +Houses with four bedrooms do sell for more than houses with three, but +one-bedroom houses have a *higher* median price than two-bedroom houses. + +Moreover, the spread within every group is far larger than the differences +across groups. + +Evidently the number of bedrooms tells us relatively little about the price of a +house. + +Notice also that the individually plotted points sit almost entirely above the +whiskers rather than below them. + +This is the right skew again, now visible group by group. + +```{exercise} +:label: obs_ex2 + +The data set also records the floor area of each house, in square feet, in the +column `living_area_sqft`. + +Split the houses into four groups of equal size according to floor area (the +Pandas function `qcut` will do this for you) and produce a box plot of sale +price for each group. + +Is floor area a better predictor of price than the number of bedrooms? +``` + +```{solution-start} obs_ex2 +:class: dropdown +``` + +Here is one solution: + +```{code-cell} ipython3 +area_quartile = pd.qcut(houses['living_area_sqft'], 4, + labels=['Q1', 'Q2', 'Q3', 'Q4']) +groups = [price[area_quartile == q] for q in ('Q1', 'Q2', 'Q3', 'Q4')] + +fig, ax = plt.subplots() +ax.boxplot(groups, tick_labels=['Q1', 'Q2', 'Q3', 'Q4']) +ax.set_xlabel('quartile of floor area') +ax.set_ylabel('sale price (US$)') +plt.show() +``` + +Now the medians increase steadily from one group to the next, and the gaps +between the groups are large relative to the spread within them. + +Floor area is clearly the better predictor. + +```{solution-end} +``` + + +(violin_plots)= +### Violin plots + + +Another way to display an observed distribution is via a violin plot. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +ax.violinplot(x_amazon) +ax.set_ylabel('monthly return (percent change)') +ax.set_xlabel('KDE') +plt.show() +``` + +Violin plots are particularly useful when we want to compare different distributions. + +For example, let's compare the monthly returns on Amazon shares with the monthly return on Costco shares. + +```{code-cell} ipython3 +:tags: [hide-output] + +df = yf.download('COST', '2000-1-1', '2024-1-1', interval='1mo') +prices = df['Close'] +x_costco = prices.pct_change()[1:] * 100 +``` + +```{code-cell} ipython3 +fig, ax = plt.subplots() +ax.violinplot([x_amazon['AMZN'], x_costco['COST']]) +ax.set_ylabel('monthly return (percent change)') +ax.set_xlabel('retailers') + +ax.set_xticks([1, 2]) +ax.set_xticklabels(['Amazon', 'Costco']) +plt.show() +``` + +## Connection to probability distributions + +Let's discuss the connection between observed distributions and probability distributions. + +Sometimes it's helpful to imagine that an observed distribution is generated by a particular probability distribution. + +For example, we might look at the returns from Amazon above and imagine that they were generated by a normal distribution. + +(Even though this is not true, it *might* be a helpful way to think about the data.) + +Here we match a normal distribution to the Amazon monthly returns by setting the +sample mean to the mean of the normal distribution and the sample variance equal +to the variance. + +Then we plot the density and the histogram. + +```{code-cell} ipython3 +μ = x_amazon.mean() +σ_squared = x_amazon.var() +σ = np.sqrt(σ_squared) +u = scipy.stats.norm(μ, σ) +``` + +```{code-cell} ipython3 +x_grid = np.linspace(-50, 65, 200) +fig, ax = plt.subplots() +ax.plot(x_grid, u.pdf(x_grid)) +ax.hist(x_amazon, density=True, bins=40) +ax.set_xlabel('monthly return (percent change)') +ax.set_ylabel('density') +plt.show() +``` + +The match between the histogram and the density is not bad but also not very good. + +One reason is that the normal distribution is not really a good fit for this observed data --- we will discuss this point again when we talk about {ref}`heavy tailed distributions`. + +Of course, if the data really *is* generated by the normal distribution, then the fit will be better. + +Let's see this in action + +- first we generate random draws from the normal distribution +- then we histogram them and compare with the density. + +```{code-cell} ipython3 +μ, σ = 0, 1 +u = scipy.stats.norm(μ, σ) +N = 2000 # Number of observations +x_draws = u.rvs(N) +x_grid = np.linspace(-4, 4, 200) +fig, ax = plt.subplots() +ax.plot(x_grid, u.pdf(x_grid)) +ax.hist(x_draws, density=True, bins=40) +ax.set_xlabel('x') +ax.set_ylabel('density') +plt.show() +``` + +Note that if you keep increasing $N$, which is the number of observations, the fit will get better and better. + +This convergence is a version of the "law of large numbers", which we will discuss {ref}`later`. diff --git a/lectures/prob_dist.md b/lectures/prob_dist.md index f94fadba..09bd21fe 100644 --- a/lectures/prob_dist.md +++ b/lectures/prob_dist.md @@ -20,21 +20,17 @@ kernelspec: In data science applications, we are often interested in data on a specific variable. -In this lecture we give a quick introduction to data and probability distributions using Python. +In this lecture we give a quick introduction to probability distributions using Python. -```{code-cell} ipython3 -:tags: [hide-output] - -!pip install --upgrade yfinance -``` +A companion lecture, {doc}`observed_distributions`, treats observed data --- sets +of numbers that we measure or collect --- and its connection to the probability +distributions studied here. ```{code-cell} ipython3 import matplotlib.pyplot as plt import pandas as pd import numpy as np -import yfinance as yf import scipy.stats -import seaborn as sns ``` To motivate what follows, let's start with a real example: the heights of adult men and women in the United States. @@ -51,9 +47,8 @@ mystnb: name: fig:us-heights tags: [hide-input] --- -# Data file is stored in this repo for now; switch to the QuantEcon/datasets -# URL once that repo exists (see QuantEcon/meta#336). -url = '_static/lecture_specific/prob_dist/us_adult_heights.csv' +url = ('https://github.com/QuantEcon/data-lectures/raw/main/' + 'lectures/us_adult_heights.csv') heights = pd.read_csv(url) male = heights[heights['sex'] == 'male']['height_cm'] female = heights[heights['sex'] == 'female']['height_cm'] @@ -176,6 +171,66 @@ $$ Variance is also called the *second central moment* of the distribution. +The **standard deviation** of $X$ is the square root of the variance: + +$$ +\sigma = \sqrt{\mathbb{V}[X]} +$$ + +We often prefer the standard deviation to the variance because it is measured in the same units as $X$ itself. + +For example, if $X$ is a height in centimeters, then $\sigma$ is in centimeters, while the variance is in centimeters squared. + +This means that $\sigma$ can be read directly off the horizontal axis of a histogram of the data, as a measure of spread. + +Means and variances are special cases of moments. + +Writing $\mu = \mathbb{E}[X]$, the $k$-th **moment** of $X$ is $\mathbb{E}[X^k]$, while the $k$-th **central moment** is $\mathbb{E}[(X - \mu)^k]$. + +Thus the mean is the first moment and the variance is the second central moment. + +It is often convenient to work with **standardized moments** + +$$ +\mathbb{E} \left[ \left( \frac{X - \mu}{\sigma} \right)^k \right] +$$ + +which are unchanged when we shift $X$ or rescale it. + +(If $X$ is measured in centimeters, we obtain the same standardized moments after converting to inches.) + +The third standardized moment is called the **skewness**: + +$$ +S = \mathbb{E} \left[ \left( \frac{X - \mu}{\sigma} \right)^3 \right] +$$ + +Skewness measures asymmetry. + +Any distribution that is symmetric about its mean has zero skewness, while a distribution with a long right tail has positive skewness. + +The fourth standardized moment measures how much probability mass sits far out in the tails. + +For *every* normal distribution this quantity equals 3, regardless of $\mu$ and $\sigma$. + +Since the normal distribution is such a useful benchmark, it is common to subtract 3 and work with the **excess kurtosis** + +$$ +K = \mathbb{E} \left[ \left( \frac{X - \mu}{\sigma} \right)^4 \right] - 3 +$$ + +so that $K = 0$ for the normal distribution. + +Positive excess kurtosis means more mass in the tails than the normal distribution --- extreme values are more likely. + +```{note} +Some authors call the fourth standardized moment itself the "kurtosis", so that the normal distribution has kurtosis 3. + +We follow SciPy, whose `scipy.stats.kurtosis` returns the excess version by default. +``` + +We will use skewness and excess kurtosis in {doc}`observed_distributions` to help judge whether a given data set looks normally distributed. + The **cumulative distribution function** (CDF) of $X$ is defined by $$ @@ -498,6 +553,22 @@ F(x) = \mathbb P\{X \leq x\} = \int_{-\infty}^x p(x) dx $$ +Skewness and excess kurtosis are defined exactly as in the discrete case. + +For the continuous distributions we study below, $F$ is strictly increasing, so it has an inverse $F^{-1}$, which is called the **quantile function**. + +Given $\tau \in (0,1)$, the value $q_\tau = F^{-1}(\tau)$ is called the $\tau$-th **quantile** of the distribution. + +It is the point such that $X$ falls below it with probability $\tau$. + +The 0.5 quantile is called the **median**, which is an alternative measure of the center of a distribution. + +The 0.25 and 0.75 quantiles are called the first and third **quartiles**, and the distance between them is the **interquartile range**, an alternative measure of spread. + +These alternatives are useful because, unlike the mean and the standard deviation, they are barely affected by a small number of extreme values. + +(We will see in {doc}`heavy_tails` that this robustness matters a great deal for some data sets.) + #### Normal distribution @@ -523,6 +594,24 @@ u = scipy.stats.norm(μ, σ) u.mean(), u.var() ``` +The `stats` method returns the skewness and excess kurtosis when we ask for moments `'sk'`: + +```{code-cell} ipython3 +u.stats(moments='sk') +``` + +Both are zero, as promised. + +(The skewness is zero because the density is symmetric about $\mu$.) + +Here are the median and the two quartiles, obtained via the `ppf` method (SciPy's name for the quantile function): + +```{code-cell} ipython3 +u.ppf(0.5), u.ppf(0.25), u.ppf(0.75) +``` + +The median equals the mean because the density is symmetric. + Here's a plot of the density --- the famous "bell-shaped curve": ```{code-cell} ipython3 @@ -587,6 +676,20 @@ u = scipy.stats.lognorm(s=σ, scale=np.exp(μ)) u.mean(), u.var() ``` +The lognormal distribution provides a sharp contrast with the normal distribution in terms of higher moments: + +```{code-cell} ipython3 +u.stats(moments='sk') +``` + +The skewness is large and positive, reflecting the long right tail, and the excess kurtosis is enormous. + +The gap between the mean and the median is correspondingly large: + +```{code-cell} ipython3 +u.mean(), u.ppf(0.5) +``` + ```{code-cell} ipython3 μ_vals = [-1, 0, 1] σ_vals = [0.25, 0.5, 1] @@ -796,260 +899,3 @@ ax.set_ylabel('CDF') plt.legend() plt.show() ``` - -## Observed distributions - - -Sometimes we refer to observed data or measurements as "distributions". - -For example, let's say we observe the income of 10 people over a year: - -```{code-cell} ipython3 -data = [['Hiroshi', 1200], - ['Ako', 1210], - ['Emi', 1400], - ['Daiki', 990], - ['Chiyo', 1530], - ['Taka', 1210], - ['Katsuhiko', 1240], - ['Daisuke', 1124], - ['Yoshi', 1330], - ['Rie', 1340]] - -df = pd.DataFrame(data, columns=['name', 'income']) -df -``` - -In this situation, we might refer to the set of their incomes as the "income distribution." - -The terminology is confusing because this set is not a probability distribution ---- it's just a collection of numbers. - -However, as we will see, there are connections between observed distributions (i.e., sets of -numbers like the income distribution above) and probability distributions. - -Below we explore some observed distributions. - - -### Summary statistics - -Suppose we have an observed distribution with values $\{x_1, \ldots, x_n\}$ - -The **sample mean** of this distribution is defined as - -$$ -\bar x = \frac{1}{n} \sum_{i=1}^n x_i -$$ - -The **sample variance** is defined as - -$$ -\frac{1}{n} \sum_{i=1}^n (x_i - \bar x)^2 -$$ - -For the income distribution given above, we can calculate these numbers via - -```{code-cell} ipython3 -x = df['income'] -x.mean(), x.var() -``` - -```{exercise} -:label: prob_ex4 - -If you try to check that the formulas given above for the sample mean and sample -variance produce the same numbers, you will see that the variance isn't quite -right. This is because SciPy uses $1/(n-1)$ instead of $1/n$ as the term at the -front of the variance. (Some books define the sample variance this way.) -Confirm. -``` - - -### Visualization - -Let's look at different ways that we can visualize one or more observed distributions. - -We will cover - -- histograms -- kernel density estimates and -- violin plots - - -#### Histograms - -We can histogram the income distribution we just constructed as follows - -```{code-cell} ipython3 -fig, ax = plt.subplots() -ax.hist(x, bins=5, density=True, histtype='bar') -ax.set_xlabel('income') -ax.set_ylabel('density') -plt.show() -``` - -Let's look at a distribution from real data. - -In particular, we will look at the monthly return on Amazon shares between 2000/1/1 and 2024/1/1. - -The monthly return is calculated as the percent change in the share price over each month. - -So we will have one observation for each month. - -```{code-cell} ipython3 -:tags: [hide-output] - -df = yf.download('AMZN', '2000-1-1', '2024-1-1', interval='1mo') -prices = df['Close'] -x_amazon = prices.pct_change()[1:] * 100 -x_amazon.head() -``` - -The first observation is the monthly return (percent change) over January 2000, which was - -```{code-cell} ipython3 -x_amazon.iloc[0] -``` - -Let's turn the return observations into an array and histogram it. - -```{code-cell} ipython3 -fig, ax = plt.subplots() -ax.hist(x_amazon, bins=20) -ax.set_xlabel('monthly return (percent change)') -ax.set_ylabel('density') -plt.show() -``` - -#### Kernel density estimates - -Kernel density estimates (KDE) provide a simple way to estimate and visualize the density of a distribution. - -If you are not familiar with KDEs, you can think of them as a smoothed -histogram. - -Let's have a look at a KDE formed from the Amazon return data. - -```{code-cell} ipython3 -fig, ax = plt.subplots() -sns.kdeplot(x_amazon, ax=ax) -ax.set_xlabel('monthly return (percent change)') -ax.set_ylabel('KDE') -plt.show() -``` - -The smoothness of the KDE is dependent on how we choose the bandwidth. - -```{code-cell} ipython3 -fig, ax = plt.subplots() -sns.kdeplot(x_amazon, ax=ax, bw_adjust=0.1, alpha=0.5, label="bw=0.1") -sns.kdeplot(x_amazon, ax=ax, bw_adjust=0.5, alpha=0.5, label="bw=0.5") -sns.kdeplot(x_amazon, ax=ax, bw_adjust=1, alpha=0.5, label="bw=1") -ax.set_xlabel('monthly return (percent change)') -ax.set_ylabel('KDE') -plt.legend() -plt.show() -``` - -When we use a larger bandwidth, the KDE is smoother. - -A suitable bandwidth is not too smooth (underfitting) or too wiggly (overfitting). - - -#### Violin plots - - -Another way to display an observed distribution is via a violin plot. - -```{code-cell} ipython3 -fig, ax = plt.subplots() -ax.violinplot(x_amazon) -ax.set_ylabel('monthly return (percent change)') -ax.set_xlabel('KDE') -plt.show() -``` - -Violin plots are particularly useful when we want to compare different distributions. - -For example, let's compare the monthly returns on Amazon shares with the monthly return on Costco shares. - -```{code-cell} ipython3 -:tags: [hide-output] - -df = yf.download('COST', '2000-1-1', '2024-1-1', interval='1mo') -prices = df['Close'] -x_costco = prices.pct_change()[1:] * 100 -``` - -```{code-cell} ipython3 -fig, ax = plt.subplots() -ax.violinplot([x_amazon['AMZN'], x_costco['COST']]) -ax.set_ylabel('monthly return (percent change)') -ax.set_xlabel('retailers') - -ax.set_xticks([1, 2]) -ax.set_xticklabels(['Amazon', 'Costco']) -plt.show() -``` - -### Connection to probability distributions - -Let's discuss the connection between observed distributions and probability distributions. - -Sometimes it's helpful to imagine that an observed distribution is generated by a particular probability distribution. - -For example, we might look at the returns from Amazon above and imagine that they were generated by a normal distribution. - -(Even though this is not true, it *might* be a helpful way to think about the data.) - -Here we match a normal distribution to the Amazon monthly returns by setting the -sample mean to the mean of the normal distribution and the sample variance equal -to the variance. - -Then we plot the density and the histogram. - -```{code-cell} ipython3 -μ = x_amazon.mean() -σ_squared = x_amazon.var() -σ = np.sqrt(σ_squared) -u = scipy.stats.norm(μ, σ) -``` - -```{code-cell} ipython3 -x_grid = np.linspace(-50, 65, 200) -fig, ax = plt.subplots() -ax.plot(x_grid, u.pdf(x_grid)) -ax.hist(x_amazon, density=True, bins=40) -ax.set_xlabel('monthly return (percent change)') -ax.set_ylabel('density') -plt.show() -``` - -The match between the histogram and the density is not bad but also not very good. - -One reason is that the normal distribution is not really a good fit for this observed data --- we will discuss this point again when we talk about {ref}`heavy tailed distributions`. - -Of course, if the data really *is* generated by the normal distribution, then the fit will be better. - -Let's see this in action - -- first we generate random draws from the normal distribution -- then we histogram them and compare with the density. - -```{code-cell} ipython3 -μ, σ = 0, 1 -u = scipy.stats.norm(μ, σ) -N = 2000 # Number of observations -x_draws = u.rvs(N) -x_grid = np.linspace(-4, 4, 200) -fig, ax = plt.subplots() -ax.plot(x_grid, u.pdf(x_grid)) -ax.hist(x_draws, density=True, bins=40) -ax.set_xlabel('x') -ax.set_ylabel('density') -plt.show() -``` - -Note that if you keep increasing $N$, which is the number of observations, the fit will get better and better. - -This convergence is a version of the "law of large numbers", which we will discuss {ref}`later`. From 966a45e3d3573db9df2c181aa8d0401313c65fdd Mon Sep 17 00:00:00 2001 From: John Stachurski Date: Mon, 3 Aug 2026 16:30:15 +1000 Subject: [PATCH 2/4] prob_dist: expectations of functions, kurtosis, structure, output MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Four fixes from review of the previous commit. Expectations of functions were used but never defined: the moment expressions all take the form E[f(X)] for some f, so that form is now defined explicitly — as a sum in the discrete section and as an integral in the continuous one — and the variance is written first in E notation and then as the sum it stands for. Kurtosis and excess kurtosis are two distinct quantities and are now defined as such: kurtosis as the fourth standardized moment (normal = 3), and excess kurtosis as that minus 3 (normal = 0). Previously the lecture defined only the excess version and treated the other name as a caveat. The note is now about software rather than authors, since the real trap is that scipy.stats.kurtosis returns the excess version despite its name. The lecture had only two top-level sections, one of which held everything. "Common distributions" is dropped as a wrapper, promoting "Discrete distributions" and "Continuous distributions" to top level and the individual families to sections within them. Scalar outputs printed as np.float64(0.0) under NumPy 2. Setting np.set_printoptions(legacy='1.25') in both lectures restores plain scalar output without affecting how arrays print. Co-Authored-By: Claude Opus 5 (1M context) --- lectures/observed_distributions.md | 19 +++++--- lectures/prob_dist.md | 78 +++++++++++++++++++----------- 2 files changed, 64 insertions(+), 33 deletions(-) diff --git a/lectures/observed_distributions.md b/lectures/observed_distributions.md index dada86ae..1d181e3e 100644 --- a/lectures/observed_distributions.md +++ b/lectures/observed_distributions.md @@ -4,7 +4,7 @@ jupytext: extension: .md format_name: myst format_version: 0.13 - jupytext_version: 1.16.6 + jupytext_version: 1.17.2 kernelspec: display_name: Python 3 (ipykernel) language: python @@ -41,6 +41,8 @@ import numpy as np import yfinance as yf import scipy.stats import seaborn as sns + +np.set_printoptions(legacy='1.25') # print scalars as plain numbers ``` Sometimes we refer to observed data or measurements as "distributions". @@ -105,16 +107,18 @@ by the observed data, weighting each observation equally. The same idea extends to higher moments. -The **sample skewness** and **sample excess kurtosis** are +The **sample skewness** and **sample kurtosis** are $$ \hat S = \frac{1}{n} \sum_{i=1}^n \left( \frac{x_i - \bar x}{s} \right)^3 \qquad \text{and} \qquad -\hat K = \frac{1}{n} \sum_{i=1}^n \left( \frac{x_i - \bar x}{s} \right)^4 - 3 +\hat K = \frac{1}{n} \sum_{i=1}^n \left( \frac{x_i - \bar x}{s} \right)^4 $$ -Recall from {doc}`prob_dist` that a normal distribution has both skewness and -excess kurtosis equal to zero. +and the sample excess kurtosis is $\hat K - 3$. + +Recall from {doc}`prob_dist` that a normal distribution has skewness zero and +excess kurtosis zero. This gives us a first, purely numerical, way to ask whether a data set looks normal. @@ -232,9 +236,12 @@ adjust the estimates in different ways. The Pandas methods `x.skew()` and `x.kurt()` apply such adjustments, so they do not agree exactly with the formulas above, while `scipy.stats.skew` and -`scipy.stats.kurtosis` use the plain $1/n$ versions by default. +`scipy.stats.kurtosis` use the plain $1/n$ versions. The differences are small when $n$ is large. + +Recall also that `scipy.stats.kurtosis` returns $\hat K - 3$ rather than +$\hat K$, which is why we read its output as the excess kurtosis. ``` diff --git a/lectures/prob_dist.md b/lectures/prob_dist.md index 09bd21fe..d4936fa1 100644 --- a/lectures/prob_dist.md +++ b/lectures/prob_dist.md @@ -31,6 +31,8 @@ import matplotlib.pyplot as plt import pandas as pd import numpy as np import scipy.stats + +np.set_printoptions(legacy='1.25') # print scalars as plain numbers ``` To motivate what follows, let's start with a real example: the heights of adult men and women in the United States. @@ -96,13 +98,9 @@ Such compact summaries are extremely useful. They are one reason we study **common distributions**: named families of distributions, each governed by a small number of parameters, that have proven useful for describing data. -We turn to these now. - -## Common distributions - -In this section we recall the definitions of some well-known distributions and explore how to manipulate them with SciPy. +We turn to these now, recalling the definitions of some well-known distributions and exploring how to manipulate them with SciPy. -### Discrete distributions +## Discrete distributions Let's start with discrete distributions. @@ -163,10 +161,22 @@ Expectation is also called the *first moment* of the distribution. We also refer to this number as the mean of the distribution (represented by) $p$. +More generally, if $f$ is a function on $S$, then $f(X)$ is a random variable that takes the value $f(x_i)$ whenever $X$ takes the value $x_i$. + +Its expectation is obtained by weighting each of these values by its probability: + +$$ +\mathbb{E}[f(X)] = \sum_{i=1}^n f(x_i) p(x_i) +$$ + +Every quantity we define below is an expectation of this form, for a suitable choice of $f$. + The **variance** of $X$ is defined as $$ -\mathbb{V}[X] = \sum_{i=1}^n (x_i - \mathbb{E}[X])^2 p(x_i) +\mathbb{V}[X] + = \mathbb{E}[(X - \mathbb{E}[X])^2] + = \sum_{i=1}^n (x_i - \mathbb{E}[X])^2 p(x_i) $$ Variance is also called the *second central moment* of the distribution. @@ -209,24 +219,32 @@ Skewness measures asymmetry. Any distribution that is symmetric about its mean has zero skewness, while a distribution with a long right tail has positive skewness. -The fourth standardized moment measures how much probability mass sits far out in the tails. +The fourth standardized moment is called the **kurtosis**: + +$$ +K = \mathbb{E} \left[ \left( \frac{X - \mu}{\sigma} \right)^4 \right] +$$ + +Kurtosis measures how much probability mass sits far out in the tails. -For *every* normal distribution this quantity equals 3, regardless of $\mu$ and $\sigma$. +For *every* normal distribution, $K = 3$, regardless of $\mu$ and $\sigma$. Since the normal distribution is such a useful benchmark, it is common to subtract 3 and work with the **excess kurtosis** $$ -K = \mathbb{E} \left[ \left( \frac{X - \mu}{\sigma} \right)^4 \right] - 3 +K - 3 $$ -so that $K = 0$ for the normal distribution. +which is zero for the normal distribution. Positive excess kurtosis means more mass in the tails than the normal distribution --- extreme values are more likely. ```{note} -Some authors call the fourth standardized moment itself the "kurtosis", so that the normal distribution has kurtosis 3. +Take care when reading software documentation, since these two names are not always used correctly. -We follow SciPy, whose `scipy.stats.kurtosis` returns the excess version by default. +For example, `scipy.stats.kurtosis` returns the excess kurtosis by default, rather than the kurtosis. + +(Set `fisher=False` to obtain the kurtosis.) ``` We will use skewness and excess kurtosis in {doc}`observed_distributions` to help judge whether a given data set looks normally distributed. @@ -243,7 +261,7 @@ Here $\mathbb 1\{ \textrm{statement} \} = 1$ if "statement" is true and zero oth Hence the second term takes all $x_i \leq x$ and sums their probabilities. -#### Uniform distribution +### Uniform distribution One simple example is the **uniform distribution**, where $p(x_i) = 1/n$ for all $i$. @@ -311,7 +329,7 @@ Check that your answers agree with `u.mean()` and `u.var()`. ``` -#### Bernoulli distribution +### Bernoulli distribution Another useful distribution is the Bernoulli distribution on $S = \{0,1\}$, which has PMF: @@ -349,7 +367,7 @@ We can evaluate the PMF as follows u.pmf(0), u.pmf(1) ``` -#### Binomial distribution +### Binomial distribution Another useful (and more interesting) distribution is the **binomial distribution** on $S=\{0, \ldots, n\}$, which has PMF: @@ -444,7 +462,7 @@ We can see that the output graph is the same as the one above. ```{solution-end} ``` -#### Geometric distribution +### Geometric distribution The geometric distribution has infinite support $S = \{0, 1, 2, \ldots\}$ and its PMF is given by @@ -484,7 +502,7 @@ ax.set_ylabel('PMF') plt.show() ``` -#### Poisson distribution +### Poisson distribution The Poisson distribution on $S = \{0, 1, \ldots\}$ with parameter $\lambda > 0$ has PMF @@ -521,7 +539,7 @@ ax.set_ylabel('PMF') plt.show() ``` -### Continuous distributions +## Continuous distributions A continuous distribution is represented by a **probability density function**, which is a function $p$ over $\mathbb R$ (the set of all real numbers) such that $p(x) \geq 0$ for all $x$ and @@ -538,7 +556,7 @@ $$ for all $a \leq b$. -The definition of the mean and variance of a random variable $X$ with distribution $p$ are the same as the discrete case, after replacing the sum with an integral. +Expectations are defined as in the discrete case, after replacing the sum with an integral. For example, the mean of $X$ is @@ -546,6 +564,14 @@ $$ \mathbb{E}[X] = \int_{-\infty}^\infty x p(x) dx $$ +while, for a function $f$, + +$$ +\mathbb{E}[f(X)] = \int_{-\infty}^\infty f(x) p(x) dx +$$ + +The variance, standard deviation, moments, skewness and kurtosis are then defined by exactly the same expressions as before. + The **cumulative distribution function** (CDF) of $X$ is defined by $$ @@ -553,8 +579,6 @@ F(x) = \mathbb P\{X \leq x\} = \int_{-\infty}^x p(x) dx $$ -Skewness and excess kurtosis are defined exactly as in the discrete case. - For the continuous distributions we study below, $F$ is strictly increasing, so it has an inverse $F^{-1}$, which is called the **quantile function**. Given $\tau \in (0,1)$, the value $q_\tau = F^{-1}(\tau)$ is called the $\tau$-th **quantile** of the distribution. @@ -570,7 +594,7 @@ These alternatives are useful because, unlike the mean and the standard deviatio (We will see in {doc}`heavy_tails` that this robustness matters a great deal for some data sets.) -#### Normal distribution +### Normal distribution Perhaps the most famous distribution is the **normal distribution**, which has density @@ -647,7 +671,7 @@ plt.legend() plt.show() ``` -#### Lognormal distribution +### Lognormal distribution The **lognormal distribution** is a distribution on $\left(0, \infty\right)$ with density @@ -723,7 +747,7 @@ plt.legend() plt.show() ``` -#### Exponential distribution +### Exponential distribution The **exponential distribution** is a distribution supported on $\left(0, \infty\right)$ with density @@ -779,7 +803,7 @@ plt.legend() plt.show() ``` -#### Beta distribution +### Beta distribution The **beta distribution** is a distribution on $(0, 1)$ with density @@ -840,7 +864,7 @@ plt.legend() plt.show() ``` -#### Gamma distribution +### Gamma distribution The **gamma distribution** is a distribution on $\left(0, \infty\right)$ with density From 693a0dcc3c430077d79bcc300eb450bd3dc56be7 Mon Sep 17 00:00:00 2001 From: John Stachurski Date: Mon, 3 Aug 2026 16:42:09 +1000 Subject: [PATCH 3/4] observed_distributions: ECDF naming, KDE over histogram, deaths violin MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Uses ECDF throughout rather than EDF, including the section heading, the helper function name and the axis labels. Drops the claim that the normal fit to the log prices misses "in the tails", which is not visible in the figure — it just says the fit is close but not perfect. Adds a KDE of the log sale prices drawn over a faded histogram of the same data, closing the KDE section by showing what "a smoothed histogram" means against the histogram it smooths. Adds a violin plot of age at death by sex, which shows what the box plot reduces away: both distributions are strongly left-skewed with a thin tail running down to young ages, and the female distribution is both shifted up and more concentrated at the top. Medians are shown, at 82 and 88. Co-Authored-By: Claude Opus 5 (1M context) --- lectures/observed_distributions.md | 61 +++++++++++++++++++++++++----- 1 file changed, 51 insertions(+), 10 deletions(-) diff --git a/lectures/observed_distributions.md b/lectures/observed_distributions.md index 1d181e3e..062e92f8 100644 --- a/lectures/observed_distributions.md +++ b/lectures/observed_distributions.md @@ -429,12 +429,12 @@ ax.set_ylabel('density') plt.show() ``` -### Empirical distribution functions +### Empirical cumulative distribution functions A histogram estimates the density of the data. -The **empirical distribution function** (EDF), also called the empirical CDF, -does the same job for the CDF. +The **empirical cumulative distribution function** (ECDF) does the same job +for the CDF. For a sample $\{x_1, \ldots, x_n\}$ it is defined as @@ -445,13 +445,13 @@ $$ In words, $F_n(x)$ is just the fraction of observations that are less than or equal to $x$. -The EDF is a step function that jumps up by $1/n$ at each observation. +The ECDF is a step function that jumps up by $1/n$ at each observation. Here is a function that plots it, obtained by sorting the data and stepping up as we move from left to right. ```{code-cell} ipython3 -def plot_edf(sample, ax, **kwargs): +def plot_ecdf(sample, ax, **kwargs): x_sorted = np.sort(sample) n = len(x_sorted) ax.step(x_sorted, np.arange(1, n+1) / n, where='post', **kwargs) @@ -461,13 +461,13 @@ Let's apply it to the house price data. ```{code-cell} ipython3 fig, ax = plt.subplots() -plot_edf(price, ax) +plot_ecdf(price, ax) ax.set_xlabel('sale price (US$)') -ax.set_ylabel('EDF') +ax.set_ylabel('ECDF') plt.show() ``` -Unlike a histogram, the EDF requires no choice of bin width --- it uses the data +Unlike a histogram, the ECDF requires no choice of bin width --- it uses the data exactly as they are. This makes it a good tool for comparing a data set with a probability @@ -481,7 +481,7 @@ u = scipy.stats.norm(log_price.mean(), log_price.std()) x_grid = np.linspace(log_price.min(), log_price.max(), 200) fig, ax = plt.subplots() -plot_edf(log_price, ax, label='EDF of log prices') +plot_ecdf(log_price, ax, label='ECDF of log prices') ax.plot(x_grid, u.cdf(x_grid), 'k--', alpha=0.7, label='normal CDF') ax.set_xlabel('log of sale price') ax.set_ylabel('probability') @@ -489,7 +489,7 @@ ax.legend() plt.show() ``` -The two curves are close, although the fit is not perfect in the tails. +The two curves are close, although the fit is not perfect. (Seaborn provides `sns.ecdfplot`, which produces the same figure with less code.) @@ -528,6 +528,23 @@ When we use a larger bandwidth, the KDE is smoother. A suitable bandwidth is not too smooth (underfitting) or too wiggly (overfitting). +Since a KDE is a smoothed histogram, it is often helpful to show the two +together. + +Here is the log sale price data, with the histogram faded into the background. + +```{code-cell} ipython3 +fig, ax = plt.subplots() +ax.hist(log_price, bins=50, density=True, alpha=0.25, color='C0') +sns.kdeplot(log_price, ax=ax, color='C0', lw=2) +ax.set_xlabel('log of sale price') +ax.set_ylabel('density') +plt.show() +``` + +The KDE traces out the shape of the histogram while smoothing away the +bin-to-bin variation. + ### Box-and-whisker plots @@ -651,6 +668,30 @@ ax.set_xticklabels(['Amazon', 'Costco']) plt.show() ``` +As a second comparison, let's return to the age at death data and separate men +from women. + +```{code-cell} ipython3 +male_deaths = np.repeat(deaths['age'], deaths['deaths_male']) +female_deaths = np.repeat(deaths['age'], deaths['deaths_female']) + +fig, ax = plt.subplots() +ax.violinplot([male_deaths, female_deaths], showmedians=True) +ax.set_ylabel('age at death') +ax.set_xlabel('sex') + +ax.set_xticks([1, 2]) +ax.set_xticklabels(['male', 'female']) +plt.show() +``` + +The violin plot shows the whole shape of each distribution, rather than the +five numbers that a box plot reduces it to. + +Here that matters: both distributions are strongly left-skewed, with a thin +tail of deaths at young ages, and the female distribution is both shifted +upwards and more concentrated at the top. + ## Connection to probability distributions Let's discuss the connection between observed distributions and probability distributions. From 5285edcaa9948d99c98556e2a6cf2b061e2f8c06 Mon Sep 17 00:00:00 2001 From: John Stachurski Date: Mon, 3 Aug 2026 17:34:03 +1000 Subject: [PATCH 4/4] observed_distributions: convergence and the role of independence MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Closes out the lecture with the material the issue asks for. "Larger samples" shows ECDFs of samples of size 10, 100 and 1000 against the CDF that generated them — the ECDF is the natural vehicle, since it estimates the CDF without a bin width or a bandwidth to choose. Sample means for the same sizes are printed against the population mean. The trailing two sentences of the previous section, which asserted this convergence and pointed at the law of large numbers, are absorbed here. "The role of independence" makes the point that the convergence is not automatic, using the degenerate sample: draw X once and set X_i = X for all i. Every X_i then has the correct distribution, so each observation is individually valid, but the ECDF is a single step at X and increasing n changes nothing — the three curves lie exactly on top of one another. A note guards against overclaiming: independence is sufficient, not necessary, and this lecture histograms monthly returns that are plainly dependent. What matters is that new observations keep bringing new information. The general question is left to lln_clt. Co-Authored-By: Claude Opus 5 (1M context) --- lectures/observed_distributions.md | 104 ++++++++++++++++++++++++++++- 1 file changed, 103 insertions(+), 1 deletion(-) diff --git a/lectures/observed_distributions.md b/lectures/observed_distributions.md index 062e92f8..0fa49e0b 100644 --- a/lectures/observed_distributions.md +++ b/lectures/observed_distributions.md @@ -752,4 +752,106 @@ plt.show() Note that if you keep increasing $N$, which is the number of observations, the fit will get better and better. -This convergence is a version of the "law of large numbers", which we will discuss {ref}`later`. +We investigate this convergence in the next section. + + +## Larger samples + +Throughout this lecture we have used observed data to say something about an +underlying distribution. + +This only works if a larger sample tells us more. + +Let's check that it does, using the ECDF, since it estimates the CDF without +requiring us to choose a bin width or a bandwidth. + +We draw samples of increasing size from a fixed distribution and compare each +ECDF with the CDF that generated it. + +```{code-cell} ipython3 +u = scipy.stats.lognorm(s=0.5) +x_grid = np.linspace(0, 5, 200) + +fig, ax = plt.subplots() +for n in (10, 100, 1000): + plot_ecdf(u.rvs(n, random_state=1234), ax, alpha=0.7, label=f'$n = {n}$') +ax.plot(x_grid, u.cdf(x_grid), 'k--', lw=2, label='true CDF') +ax.set_xlabel('x') +ax.set_ylabel('probability') +ax.legend() +plt.show() +``` + +The ECDF is ragged when $n = 10$ and almost indistinguishable from the true CDF +by the time $n = 1000$. + +The sample moments behave the same way. + +```{code-cell} ipython3 +for n in (10, 100, 1000, 1_000_000): + x_draws = u.rvs(n, random_state=1234) + print(f'n = {n:>9,}: sample mean = {x_draws.mean():.4f}') +print(f'{"":16}population mean = {u.mean():.4f}') +``` + +This convergence is a version of the *law of large numbers*, which we discuss +in {doc}`lln_clt`. + + +### The role of independence + +The convergence above is not automatic. + +It depends on a property of the sample that is easy to overlook, because +`rvs` supplies it silently: the draws it returns are **independent**. + +To see why this matters, suppose we take a single draw $X$ from our +distribution and then set + +$$ +X_i = X +\qquad \text{for } i = 1, \ldots, n +$$ + +Every $X_i$ now has exactly the right distribution. + +Judged one at a time, these are perfectly good observations. + +But they are useless as a sample, as the next figure shows. + +```{code-cell} ipython3 +x = u.rvs(random_state=1234) # a single draw + +fig, ax = plt.subplots() +for n in (10, 100, 1000): + x_draws = np.full(n, x) # repeated n times + plot_ecdf(x_draws, ax, alpha=0.7, label=f'$n = {n}$') +ax.plot(x_grid, u.cdf(x_grid), 'k--', lw=2, label='true CDF') +ax.set_xlabel('x') +ax.set_ylabel('probability') +ax.legend() +plt.show() +``` + +The three ECDFs lie exactly on top of one another: each is a single step at +$X$, and increasing $n$ changes nothing. + +The sample never approaches the distribution it came from, no matter how large +we make it. + +The reason is that the observations after the first one carry no information we +did not already have. + +```{note} +Independence is a clean sufficient condition rather than a necessary one. + +Many dependent samples work perfectly well --- the monthly returns we +histogrammed above are certainly not independent, since volatile months tend to +follow volatile months. + +What matters is that new observations keep bringing new information, which the +example above destroys entirely. + +The general question of what a sample can tell us about its distribution is +taken up in {doc}`lln_clt`. +```