DATA606_Lab3
LeTiciaC
March 1, 2018
Start Lab
library(DATA606)##
## Welcome to CUNY DATA606 Statistics and Probability for Data Analytics
## This package is designed to support this course. The text book used
## is OpenIntro Statistics, 3rd Edition. You can read this by typing
## vignette('os3') or visit www.OpenIntro.org.
##
## The getLabs() function will return a list of the labs available.
##
## The demo(package='DATA606') will list the demos that are available.##
## Attaching package: 'DATA606'## The following object is masked from 'package:utils':
##
## demoload("more/bdims.RData")Looking at the first few rows of data
head(bdims)## bia.di bii.di bit.di che.de che.di elb.di wri.di kne.di ank.di sho.gi
## 1 42.9 26.0 31.5 17.7 28.0 13.1 10.4 18.8 14.1 106.2
## 2 43.7 28.5 33.5 16.9 30.8 14.0 11.8 20.6 15.1 110.5
## 3 40.1 28.2 33.3 20.9 31.7 13.9 10.9 19.7 14.1 115.1
## 4 44.3 29.9 34.0 18.4 28.2 13.9 11.2 20.9 15.0 104.5
## 5 42.5 29.9 34.0 21.5 29.4 15.2 11.6 20.7 14.9 107.5
## 6 43.3 27.0 31.5 19.6 31.3 14.0 11.5 18.8 13.9 119.8
## che.gi wai.gi nav.gi hip.gi thi.gi bic.gi for.gi kne.gi cal.gi ank.gi
## 1 89.5 71.5 74.5 93.5 51.5 32.5 26.0 34.5 36.5 23.5
## 2 97.0 79.0 86.5 94.8 51.5 34.4 28.0 36.5 37.5 24.5
## 3 97.5 83.2 82.9 95.0 57.3 33.4 28.8 37.0 37.3 21.9
## 4 97.0 77.8 78.8 94.0 53.0 31.0 26.2 37.0 34.8 23.0
## 5 97.5 80.0 82.5 98.5 55.4 32.0 28.4 37.7 38.6 24.4
## 6 99.9 82.5 80.1 95.3 57.5 33.0 28.0 36.6 36.1 23.5
## wri.gi age wgt hgt sex
## 1 16.5 21 65.6 174.0 1
## 2 17.0 23 71.8 175.3 1
## 3 16.9 28 80.7 193.5 1
## 4 16.6 23 72.6 186.5 1
## 5 18.0 22 78.8 187.2 1
## 6 16.9 21 74.8 181.5 1create 2 additional data sets for males and females
mdims <- subset(bdims, sex == 1)
fdims <- subset(bdims, sex == 0)
mdims## bia.di bii.di bit.di che.de che.di elb.di wri.di kne.di ank.di sho.gi
## 1 42.9 26.0 31.5 17.7 28.0 13.1 10.4 18.8 14.1 106.2
## 2 43.7 28.5 33.5 16.9 30.8 14.0 11.8 20.6 15.1 110.5
## 3 40.1 28.2 33.3 20.9 31.7 13.9 10.9 19.7 14.1 115.1
## 4 44.3 29.9 34.0 18.4 28.2 13.9 11.2 20.9 15.0 104.5
## 5 42.5 29.9 34.0 21.5 29.4 15.2 11.6 20.7 14.9 107.5
## 6 43.3 27.0 31.5 19.6 31.3 14.0 11.5 18.8 13.9 119.8
## 7 43.5 30.0 34.0 21.9 31.7 16.1 12.5 20.8 15.6 123.5
## 8 44.4 29.8 33.2 21.8 28.8 15.1 11.9 21.0 14.6 120.4
## 9 43.5 26.5 32.1 15.5 27.5 14.1 11.2 18.9 13.2 111.0
## 10 42.0 28.0 34.0 22.5 28.0 15.6 12.0 21.1 15.0 119.5
## 11 40.3 29.0 33.0 20.1 30.3 13.4 10.4 19.4 14.5 117.1
## 12 43.7 29.0 31.3 20.5 29.7 15.0 11.7 20.9 16.0 123.5
## 13 47.4 29.6 35.7 20.8 31.4 16.1 11.3 21.5 15.4 116.5
## 14 40.3 27.5 31.4 21.7 28.0 13.3 10.3 18.8 13.2 113.0
## 15 41.0 26.8 32.2 21.9 28.6 14.9 10.6 17.8 14.0 107.5
## 16 45.0 27.0 33.2 21.7 30.6 13.7 11.1 20.7 14.0 112.0
## 17 39.9 30.0 34.5 21.0 29.4 15.6 11.9 21.2 16.0 112.2
## 18 43.0 26.5 30.3 19.3 30.0 14.8 11.2 19.7 14.7 120.0
## 19 43.1 28.6 33.4 22.2 29.5 14.9 12.2 20.8 14.8 109.0
## 20 43.6 29.3 34.4 20.2 32.6 15.4 10.9 20.7 15.5 118.5
## 21 42.0 27.5 30.7 21.3 32.0 13.1 11.1 19.2 13.9 116.0
## 22 43.8 28.0 33.3 20.0 32.0 15.0 11.5 20.4 14.4 111.0
## 23 42.3 26.4 31.2 18.0 30.9 14.6 10.8 18.6 13.8 117.7
## 24 42.7 29.9 35.0 21.8 32.8 14.3 11.2 19.8 14.1 123.9
## 25 44.8 27.8 32.2 18.3 31.5 15.2 11.6 19.4 14.7 120.6
## 26 46.0 30.1 34.5 20.2 31.1 16.4 13.3 22.2 14.9 129.5
## 27 45.4 31.8 35.2 20.2 32.3 14.6 10.5 20.2 15.3 115.0
## 28 40.5 28.3 33.4 19.2 28.8 14.6 11.1 20.8 14.5 116.0
## 29 39.4 25.5 30.2 17.6 27.7 13.0 10.2 18.9 13.2 107.8
## 30 40.2 27.2 31.7 18.1 26.5 13.3 10.1 18.6 13.2 100.2
## 31 44.2 30.3 34.7 19.4 30.0 14.9 11.0 19.1 15.8 113.0
## 32 41.0 23.6 30.2 22.9 28.0 14.3 11.2 18.2 14.0 117.9
## 33 44.0 31.0 35.3 19.2 31.0 15.2 11.4 21.2 15.1 112.5
## 34 41.6 32.0 35.3 23.6 27.0 15.5 11.3 20.9 15.0 110.5
## 35 41.0 25.1 31.9 20.8 27.9 13.6 10.8 18.8 12.9 112.0
## 36 41.5 24.5 30.5 17.7 26.7 13.3 10.8 18.6 14.0 104.0
## 37 41.1 27.8 31.4 19.0 31.5 14.5 11.9 18.5 13.0 114.8
## 38 38.8 27.2 31.6 18.5 25.5 13.4 10.8 19.0 14.0 108.0
## 39 36.2 27.5 30.4 18.7 28.0 13.6 10.8 19.0 15.4 111.2
## 40 42.1 27.5 32.4 18.2 28.0 16.2 12.0 21.0 16.4 118.3
## 41 40.3 29.4 32.9 23.7 31.5 14.6 11.3 19.8 15.2 115.2
## 42 41.7 27.1 32.6 21.6 28.0 14.1 11.5 19.7 13.8 129.9
## 43 37.8 27.1 31.5 18.5 27.3 14.6 10.8 19.5 14.9 112.9
## 44 39.2 26.1 30.8 19.4 29.9 14.3 11.2 20.0 16.0 112.2
## 45 41.5 30.8 33.3 19.4 30.6 14.8 11.3 20.2 16.0 117.1
## 46 42.5 27.8 33.5 20.6 30.2 15.9 12.8 22.4 16.3 118.7
## 47 39.4 26.1 34.4 20.4 27.3 15.1 10.6 20.0 15.3 109.2
## 48 43.6 33.1 33.5 21.6 33.1 15.6 12.0 20.7 16.5 128.1
## 49 38.9 24.9 28.7 19.7 26.8 14.2 10.2 18.0 14.4 113.3
## 50 37.6 24.4 28.0 18.0 26.4 14.2 10.6 17.3 13.4 108.4
## 51 39.4 28.3 30.6 20.2 28.7 15.0 11.5 18.4 14.4 118.7
## 52 38.5 26.1 30.8 20.6 30.8 15.1 11.4 19.8 14.2 126.3
## 53 40.1 27.8 33.1 19.2 31.3 15.4 11.5 20.6 15.4 124.2
## 54 40.3 28.0 32.0 20.9 31.7 14.8 10.6 19.4 15.0 126.7
## 55 37.6 26.6 29.9 17.3 25.6 12.8 10.0 17.0 13.0 103.3
## 56 38.3 25.2 30.2 17.0 26.4 13.2 10.4 18.8 13.0 101.2
## 57 39.7 28.6 32.1 19.1 27.1 13.4 10.0 18.2 14.8 104.3
## 58 42.2 29.0 33.7 22.5 30.4 15.6 12.0 19.8 16.2 113.2
## 59 41.1 30.4 35.1 23.2 32.6 15.5 11.6 21.5 15.4 121.9
## 60 40.5 29.3 33.7 19.6 29.8 13.8 11.7 19.7 14.4 113.1
## 61 41.5 28.6 30.4 20.8 26.9 14.8 11.2 20.7 16.5 108.5
## 62 43.4 32.4 36.4 20.3 32.1 15.6 12.0 20.8 16.3 113.9
## 63 43.5 26.0 31.6 19.1 30.9 14.3 11.4 19.5 14.6 112.6
## 64 41.3 27.1 32.4 17.5 27.6 14.1 10.8 20.2 15.5 110.2
## 65 40.3 29.5 33.3 18.4 26.2 14.0 11.0 19.4 14.8 108.7
## 66 36.3 29.2 33.0 20.0 29.0 14.1 11.7 20.4 14.3 104.0
## 67 39.9 28.3 32.0 18.3 31.4 13.5 11.4 18.9 14.4 115.2
## 68 39.8 28.8 33.0 19.7 28.7 12.4 10.7 18.5 13.2 111.9
## 69 43.5 33.2 34.0 23.9 34.3 15.8 12.0 18.6 13.2 127.0
## 70 41.2 26.6 30.6 19.5 28.0 13.1 10.4 19.0 13.8 111.2
## 71 44.0 28.4 32.0 22.5 29.7 14.9 10.9 21.0 14.8 122.0
## 72 41.8 28.5 31.6 21.6 31.5 13.3 10.3 18.9 14.3 114.5
## 73 42.9 27.5 30.3 18.9 29.6 12.6 10.4 19.2 13.8 109.5
## 74 38.7 24.6 28.5 18.3 29.8 14.0 11.2 18.9 13.6 110.8
## 75 41.4 26.4 32.3 18.6 31.3 14.9 11.5 18.9 14.6 118.8
## 76 39.6 27.5 30.2 19.2 28.9 13.5 10.4 19.3 14.2 108.0
## 77 40.5 27.5 32.3 19.4 28.8 12.6 10.6 18.4 14.0 114.3
## 78 34.1 28.1 30.1 21.8 25.8 12.9 9.9 18.6 12.3 105.4
## 79 43.5 28.8 34.0 20.6 29.0 14.3 10.5 19.8 14.2 115.0
## 80 44.1 29.2 35.3 23.6 30.9 15.8 12.5 20.2 15.2 119.5
## 81 42.2 32.6 36.6 22.4 34.5 14.1 11.1 18.2 13.9 130.0
## 82 42.2 30.1 31.4 21.2 29.7 14.0 11.6 21.6 14.1 113.3
## 83 43.0 26.5 31.6 20.6 29.5 13.4 10.4 18.8 13.6 113.2
## 84 39.8 28.7 33.3 19.3 29.2 13.5 11.6 19.5 14.6 106.9
## 85 37.7 29.7 32.7 20.2 28.8 13.3 11.1 18.3 13.2 113.8
## 86 39.6 27.9 33.3 20.2 29.5 12.6 10.7 18.5 12.9 117.3
## 87 43.2 26.3 30.5 19.7 30.6 14.4 12.3 20.2 13.6 124.2
## 88 44.3 28.2 32.2 21.2 31.8 14.2 11.6 20.0 14.4 123.0
## 89 43.3 28.2 33.0 19.4 31.6 13.8 11.1 17.8 13.2 117.8
## 90 42.8 27.5 31.5 19.2 31.8 14.1 11.1 19.1 14.7 118.8
## 91 41.5 30.0 33.4 19.1 29.4 14.8 11.0 19.8 13.8 112.0
## 92 42.0 27.6 32.2 19.7 29.4 13.9 10.0 18.7 13.8 113.0
## 93 41.2 27.1 29.8 20.1 31.0 12.9 11.6 18.8 13.5 116.0
## 94 43.8 29.5 31.2 18.2 29.5 13.1 10.3 19.1 13.2 112.8
## 95 46.2 31.0 36.0 25.0 33.1 14.6 12.0 20.9 15.1 125.0
## 96 40.4 28.6 31.4 19.8 27.6 13.9 10.1 20.0 13.4 108.3
## 97 40.8 27.1 29.4 17.8 29.4 13.3 10.4 18.5 12.8 108.2
## 98 43.9 27.0 33.5 22.3 31.0 13.2 10.4 19.1 13.1 113.0
## 99 44.2 27.9 32.0 21.6 32.9 14.3 11.0 21.1 14.9 115.0
## 100 41.6 28.0 35.0 24.2 31.0 13.4 11.2 20.6 14.4 123.0
## 101 38.1 30.1 33.2 21.6 31.3 14.2 12.3 19.2 15.2 120.2
## 102 42.0 28.0 33.0 18.1 28.4 14.3 11.1 20.2 15.2 114.0
## 103 37.0 27.3 31.1 18.2 25.0 13.2 10.5 18.7 13.4 102.9
## 104 41.6 27.5 32.0 18.1 29.5 13.8 10.7 19.0 13.9 112.5
## 105 40.1 19.4 28.0 17.1 26.8 13.0 10.6 16.9 12.6 104.5
## 106 38.7 25.2 28.8 19.1 25.6 13.0 10.2 17.9 13.5 111.3
## 107 37.4 29.9 33.5 22.3 30.8 14.4 11.5 20.5 16.8 117.2
## 108 41.7 28.0 32.9 19.4 29.7 14.6 11.0 19.5 15.3 112.8
## 109 38.0 27.1 28.3 18.2 25.9 13.8 11.0 18.9 14.8 104.8
## 110 40.5 24.9 29.7 19.0 30.2 14.4 11.8 19.5 14.9 117.7
## 111 35.6 28.5 29.4 17.7 25.2 14.0 10.8 19.1 15.0 107.7
## 112 43.6 30.2 32.4 21.8 33.1 15.2 11.3 19.8 15.2 125.2
## 113 37.6 24.4 28.3 17.7 24.7 12.9 10.8 18.0 14.3 109.1
## 114 41.1 31.7 34.2 22.8 34.0 13.8 11.8 19.4 15.4 122.6
## 115 42.1 30.6 34.0 22.1 30.6 15.0 11.4 20.2 15.4 117.3
## 116 40.5 28.3 32.4 19.4 27.8 13.4 11.0 19.0 14.5 109.1
## 117 40.9 28.5 31.3 21.1 29.7 14.3 11.7 19.0 15.6 116.7
## 118 43.0 30.6 33.8 23.3 35.3 15.6 12.0 21.6 16.4 124.9
## 119 40.5 27.8 31.1 21.8 30.6 15.0 11.6 20.4 15.2 118.6
## 120 41.9 25.4 30.2 14.4 26.8 12.6 9.8 18.8 13.6 108.8
## 121 42.1 28.5 33.1 20.2 30.6 15.6 12.2 19.7 15.6 121.9
## 122 43.8 29.2 32.6 18.7 30.4 14.6 11.7 20.0 15.2 117.3
## 123 42.1 28.5 31.7 19.4 28.0 14.0 11.3 19.0 14.4 115.0
## 124 43.4 32.0 36.2 23.5 35.6 16.1 12.6 23.0 16.3 134.8
## 125 38.7 26.8 31.5 21.4 27.8 13.8 10.8 18.2 13.3 113.8
## 126 39.6 28.7 32.4 18.2 28.3 15.2 11.8 19.6 14.8 119.4
## 127 43.4 30.6 32.9 21.6 28.3 15.0 12.0 20.5 17.2 117.9
## 128 40.5 29.7 31.7 22.1 32.6 15.2 11.3 21.2 15.2 127.3
## 129 40.3 30.4 34.2 21.1 34.0 13.6 12.0 19.2 13.8 118.8
## 130 44.2 30.6 33.8 22.1 32.4 15.3 11.5 20.9 16.5 122.4
## 131 41.3 26.8 32.2 21.4 31.1 13.6 11.0 19.1 15.0 111.5
## 132 39.8 25.6 31.3 23.5 32.0 14.0 11.2 21.2 16.4 113.2
## 133 41.3 29.0 32.2 25.2 30.8 14.4 11.0 19.7 15.8 115.3
## 134 38.9 27.5 32.9 22.5 33.3 14.6 11.0 20.5 15.3 122.5
## 135 41.1 25.6 29.9 23.3 25.2 14.1 10.7 19.0 15.1 114.4
## 136 41.5 30.6 35.8 21.1 28.0 15.0 11.8 21.0 15.6 112.8
## 137 38.5 27.8 31.7 19.7 26.4 13.1 11.0 18.4 14.8 112.2
## 138 39.4 29.7 33.1 23.0 30.4 14.2 11.6 20.4 15.0 119.4
## 139 40.9 26.1 27.5 20.2 28.0 13.2 10.4 18.6 14.8 108.4
## 140 41.1 23.0 29.4 21.8 30.6 15.0 10.8 19.3 14.5 122.4
## 141 43.6 28.0 32.4 27.5 33.5 14.6 11.7 21.4 15.1 128.8
## 142 39.8 29.0 34.9 22.5 28.3 14.3 11.7 19.8 15.4 118.0
## 143 42.1 27.8 31.7 20.2 28.7 14.3 11.5 19.6 15.6 116.5
## 144 41.1 27.1 33.8 24.9 29.4 14.4 12.4 18.0 15.1 120.4
## 145 44.2 30.4 36.5 21.6 31.5 15.4 11.6 20.4 15.4 123.1
## 146 38.9 26.8 31.5 20.4 29.0 13.6 10.8 18.9 15.2 117.2
## 147 40.1 28.7 32.2 18.0 29.4 15.2 11.8 20.7 15.4 113.0
## 148 38.7 26.8 31.5 18.0 27.8 12.9 10.4 18.0 14.3 109.4
## 149 35.6 26.4 30.8 19.2 29.4 14.6 11.5 19.6 15.3 105.7
## 150 40.5 26.8 30.6 21.4 32.4 15.0 11.8 20.4 15.8 119.7
## 151 41.1 25.4 32.0 21.6 28.7 14.3 12.4 19.6 14.3 118.0
## 152 38.7 26.1 29.2 18.2 24.9 13.6 10.4 17.6 14.2 104.3
## 153 38.9 27.1 30.4 20.4 28.7 14.8 11.7 19.4 14.6 114.1
## 154 39.4 29.7 33.1 22.3 31.5 15.6 12.0 19.5 14.8 119.0
## 155 37.6 27.8 32.2 20.2 31.3 14.6 11.0 21.5 15.8 113.8
## 156 39.8 25.9 31.3 19.4 29.2 14.3 11.2 18.7 14.3 118.0
## 157 40.3 27.3 30.4 20.4 29.0 15.0 11.3 19.1 14.6 116.0
## 158 40.3 25.2 29.2 18.7 28.5 13.2 10.2 18.9 14.3 108.3
## 159 43.8 30.4 34.9 24.0 33.3 15.4 11.6 17.8 14.6 129.2
## 160 41.1 27.8 32.9 18.0 26.8 14.6 11.2 19.5 15.8 109.2
## 161 41.7 30.6 34.7 24.9 32.0 14.9 10.8 18.9 14.1 124.3
## 162 45.4 30.8 35.6 20.9 29.7 15.2 10.8 18.6 15.0 122.6
## 163 43.0 30.8 34.7 22.1 32.2 16.0 13.2 19.5 16.1 122.4
## 164 41.1 25.4 30.4 19.2 29.9 14.8 10.6 18.7 15.2 114.9
## 165 41.1 29.2 31.5 19.7 29.9 14.8 11.0 18.0 15.0 111.1
## 166 45.2 32.2 36.0 22.5 33.5 15.8 11.3 20.5 14.8 126.0
## 167 39.8 34.7 34.7 23.5 30.2 14.8 10.6 20.6 14.3 115.5
## 168 39.6 28.7 32.0 20.2 32.9 14.3 11.5 19.6 15.1 124.7
## 169 42.3 30.2 34.4 25.4 32.2 15.2 10.7 18.8 14.8 125.3
## 170 40.9 29.0 32.2 20.2 29.2 13.8 10.4 18.4 14.4 118.2
## 171 39.8 28.0 34.2 23.3 31.5 14.0 11.0 19.7 13.8 124.3
## 172 42.3 27.1 31.7 17.3 29.4 14.4 11.6 21.2 15.8 118.3
## 173 42.3 26.8 32.0 25.4 28.7 15.0 11.2 18.4 14.4 122.3
## 174 40.5 28.7 30.4 22.1 29.2 14.3 11.2 18.5 14.5 116.5
## 175 42.7 28.5 36.7 23.7 30.8 15.8 12.9 19.3 16.0 123.0
## 176 43.6 30.8 33.3 20.4 29.7 14.3 10.9 19.6 15.4 117.6
## 177 42.5 31.3 33.1 19.4 32.0 14.8 11.3 20.1 15.5 117.5
## 178 41.3 30.8 33.3 22.5 28.3 13.0 10.5 19.7 13.4 117.3
## 179 41.3 24.7 35.4 22.5 30.2 14.8 11.3 20.4 16.0 114.5
## 180 42.3 26.6 33.3 23.3 28.7 14.2 11.1 19.5 14.3 122.9
## 181 36.9 25.9 31.7 19.9 27.3 14.8 10.6 19.4 14.3 115.5
## 182 40.3 28.5 35.1 19.2 32.0 14.8 12.0 21.2 16.2 116.1
## 183 40.1 26.4 32.0 21.4 32.6 14.8 12.0 20.0 15.2 121.6
## 184 43.2 31.3 34.0 23.0 32.6 15.7 11.5 20.5 15.2 131.6
## 185 45.0 29.0 33.3 25.4 30.8 15.4 11.0 18.8 15.0 124.5
## 186 42.1 29.7 35.6 23.5 31.3 14.3 11.0 18.2 14.8 115.6
## 187 40.9 28.7 33.5 23.7 30.2 15.8 11.6 19.3 16.8 117.0
## 188 41.3 27.3 32.2 20.2 28.3 13.8 11.4 18.0 13.0 108.6
## 189 42.1 29.7 32.9 24.9 30.8 15.3 11.5 19.2 14.6 120.2
## 190 45.2 29.7 33.8 19.9 32.0 15.5 11.8 19.6 16.1 116.2
## 191 42.1 31.1 34.9 22.1 31.3 15.2 11.0 19.0 14.4 115.4
## 192 41.2 29.8 32.2 22.4 29.8 15.6 11.2 19.6 14.8 120.0
## 193 41.7 29.2 33.8 19.2 29.7 13.8 10.7 18.6 14.2 110.3
## 194 43.0 29.4 33.8 24.7 31.5 14.2 11.2 19.4 14.2 119.7
## 195 41.7 28.5 33.8 23.5 32.9 15.6 12.0 18.4 16.3 123.5
## 196 38.0 29.7 34.0 22.8 27.3 13.1 10.8 17.3 15.5 107.8
## 197 41.9 27.8 33.3 19.0 28.7 15.1 11.3 19.2 14.9 118.7
## 198 40.7 28.0 35.3 19.4 31.7 14.4 10.7 18.6 14.4 120.7
## 199 41.3 29.7 34.7 22.8 32.0 15.5 11.2 18.4 15.6 118.7
## 200 40.9 28.7 32.9 21.6 30.6 15.0 11.0 18.7 13.8 118.0
## 201 41.7 26.8 32.0 19.7 27.8 14.0 10.5 18.4 14.6 105.0
## 202 41.3 31.1 34.9 26.4 30.2 15.0 11.6 18.8 15.8 110.6
## 203 41.1 27.8 32.0 21.1 30.6 14.8 11.4 17.6 14.2 123.1
## 204 43.4 27.3 34.7 19.9 31.3 14.0 11.2 20.2 14.3 121.0
## 205 40.7 27.8 34.0 21.1 29.4 15.6 12.0 21.2 16.4 111.7
## 206 42.5 25.2 30.6 20.9 30.4 15.3 11.4 18.9 13.8 111.0
## 207 40.3 28.3 30.6 18.2 29.2 12.9 10.6 20.2 14.2 112.0
## 208 39.8 27.8 32.9 22.3 29.7 16.6 11.8 20.8 15.3 115.9
## 209 39.8 28.3 30.4 19.7 30.2 12.9 11.0 18.6 12.7 121.0
## 210 40.5 29.9 34.9 21.4 32.9 14.5 11.7 20.4 15.0 123.6
## 211 41.1 26.8 32.4 20.2 31.1 14.4 11.8 20.4 15.2 120.0
## 212 42.5 29.4 34.2 23.5 34.7 15.1 11.8 21.8 15.8 128.7
## 213 42.5 29.4 34.4 19.9 34.0 14.5 11.0 21.3 14.4 124.5
## 214 38.5 24.4 30.4 18.0 29.9 14.3 10.1 18.3 13.2 112.4
## 215 43.8 29.2 35.6 19.9 28.3 14.8 12.8 20.7 14.3 112.2
## 216 41.5 29.0 33.3 21.4 32.4 15.3 11.0 20.6 15.0 127.0
## 217 40.3 27.8 33.5 20.6 29.9 15.3 11.2 20.4 13.8 115.3
## 218 40.3 30.2 32.2 20.6 29.2 14.5 11.5 20.0 16.9 111.5
## 219 42.1 27.1 32.2 20.2 30.6 13.7 10.8 18.9 14.3 118.3
## 220 42.1 31.3 35.1 20.6 31.1 16.7 12.0 21.0 15.1 118.0
## 221 38.9 29.4 33.3 24.2 33.5 14.2 12.8 20.6 15.5 127.0
## 222 44.4 24.0 30.2 20.6 32.0 14.2 11.2 20.2 14.5 124.4
## 223 40.9 24.4 28.7 18.7 29.0 14.3 11.4 17.8 14.6 112.4
## 224 42.1 28.7 33.5 25.2 29.4 14.3 11.5 18.0 13.8 125.8
## 225 43.0 27.1 33.5 25.2 31.5 15.2 11.8 19.3 15.1 131.7
## 226 38.0 27.1 32.2 20.6 28.0 13.9 10.3 19.1 14.0 117.3
## 227 37.1 24.2 30.6 17.7 27.8 13.8 11.0 17.8 14.6 107.6
## 228 41.1 24.0 29.4 21.6 30.8 13.6 11.7 18.8 14.6 122.4
## 229 40.9 24.4 30.6 19.7 29.9 13.8 11.5 19.0 15.1 117.0
## 230 38.9 27.1 31.7 21.6 29.7 15.0 12.2 20.5 15.2 119.0
## 231 40.9 28.3 34.0 23.7 28.5 14.3 12.0 19.0 14.3 123.5
## 232 39.2 26.8 34.0 23.7 30.8 14.2 11.2 19.1 14.5 121.4
## 233 41.7 26.6 31.5 19.9 29.9 14.6 11.2 19.2 14.8 112.3
## 234 39.4 26.6 31.7 24.0 31.1 13.8 11.8 20.0 15.8 113.2
## 235 40.1 26.4 32.0 21.8 30.2 15.8 12.4 20.7 15.8 121.7
## 236 38.9 25.6 32.9 21.1 29.0 15.6 10.6 20.2 14.8 116.6
## 237 38.9 26.4 31.7 21.6 27.8 14.4 11.3 19.6 14.8 117.8
## 238 41.7 26.4 31.1 20.2 28.3 14.6 10.2 18.4 15.3 118.0
## 239 43.2 26.8 32.6 22.1 32.9 15.4 12.0 20.5 16.8 131.1
## 240 40.5 29.2 33.5 23.7 31.1 15.2 11.3 20.0 16.1 121.4
## 241 39.2 23.5 29.9 19.7 29.0 15.4 11.5 19.0 14.8 116.3
## 242 40.9 25.4 32.0 20.6 30.2 16.1 11.5 19.3 15.8 121.8
## 243 41.7 27.3 31.5 21.8 29.7 14.9 11.8 18.9 13.6 118.2
## 244 43.8 32.2 38.0 25.4 32.0 16.0 10.7 21.0 16.8 126.3
## 245 41.9 28.0 33.1 26.4 29.9 15.6 11.5 21.2 15.9 121.0
## 246 43.0 27.8 34.2 21.4 31.5 14.3 11.1 21.0 14.8 123.1
## 247 41.5 28.5 33.5 19.7 29.4 14.5 10.5 19.4 15.3 114.9
## che.gi wai.gi nav.gi hip.gi thi.gi bic.gi for.gi kne.gi cal.gi ank.gi
## 1 89.5 71.5 74.5 93.5 51.5 32.5 26.0 34.5 36.5 23.5
## 2 97.0 79.0 86.5 94.8 51.5 34.4 28.0 36.5 37.5 24.5
## 3 97.5 83.2 82.9 95.0 57.3 33.4 28.8 37.0 37.3 21.9
## 4 97.0 77.8 78.8 94.0 53.0 31.0 26.2 37.0 34.8 23.0
## 5 97.5 80.0 82.5 98.5 55.4 32.0 28.4 37.7 38.6 24.4
## 6 99.9 82.5 80.1 95.3 57.5 33.0 28.0 36.6 36.1 23.5
## 7 106.9 82.0 84.0 101.0 60.9 42.4 32.3 40.1 40.3 23.6
## 8 102.5 76.8 80.5 98.0 56.0 34.1 28.0 39.2 36.7 22.5
## 9 91.0 68.5 69.0 89.5 50.0 33.0 26.0 35.5 35.0 22.0
## 10 93.5 77.5 81.5 99.8 59.8 36.5 29.2 38.3 38.6 22.2
## 11 97.7 81.9 81.0 98.4 60.5 34.6 27.9 38.9 40.1 23.2
## 12 99.5 82.6 82.5 95.0 58.5 38.5 30.4 39.0 38.4 24.3
## 13 103.0 85.0 94.5 103.0 59.0 33.5 29.0 40.5 40.0 26.0
## 14 99.6 85.6 89.2 98.0 59.1 35.6 29.0 35.8 36.0 21.5
## 15 101.5 78.0 89.5 95.0 57.0 36.0 29.0 34.5 35.0 22.0
## 16 104.1 82.0 84.0 97.0 56.0 34.5 29.5 39.0 35.7 24.0
## 17 100.0 88.3 93.5 105.0 65.8 37.0 28.8 40.9 41.7 24.2
## 18 93.8 73.6 74.9 90.1 54.1 31.2 26.9 36.4 35.6 22.0
## 19 98.5 78.5 86.0 94.5 55.0 34.5 28.5 38.0 36.5 23.0
## 20 104.0 87.3 88.0 101.1 59.5 37.0 30.5 39.8 42.0 26.5
## 21 100.0 92.0 91.0 98.0 57.5 32.0 27.6 37.5 35.2 21.0
## 22 100.0 80.0 83.7 99.5 57.0 37.0 30.0 37.5 35.5 23.0
## 23 99.0 74.5 75.9 92.2 53.4 31.2 26.9 36.2 33.3 23.5
## 24 101.0 90.6 89.6 101.2 59.5 37.0 28.3 35.4 40.6 22.9
## 25 101.6 81.4 81.6 98.8 61.3 39.4 31.9 38.5 41.2 22.8
## 26 108.8 89.5 89.5 106.0 59.5 37.5 30.1 39.9 41.5 23.5
## 27 100.0 85.0 94.5 105.0 62.0 35.5 28.5 38.0 40.0 23.5
## 28 88.0 73.5 77.7 97.0 56.3 32.5 27.8 39.0 38.2 23.5
## 29 88.7 75.8 83.0 89.0 52.6 31.2 26.5 37.0 37.4 21.5
## 30 84.5 74.0 81.0 93.5 50.5 27.5 24.8 34.0 32.8 21.0
## 31 93.6 77.5 82.1 95.0 56.5 32.8 26.2 37.6 36.3 21.0
## 32 105.0 74.0 72.0 90.0 54.2 34.1 28.6 36.2 36.6 22.4
## 33 90.9 74.0 78.8 96.4 51.8 29.8 27.0 36.4 34.6 22.9
## 34 91.2 82.0 89.5 100.0 57.5 32.8 28.0 40.7 40.1 24.3
## 35 98.4 73.0 83.0 95.4 56.3 36.4 27.5 37.2 34.5 21.8
## 36 85.0 70.5 84.0 90.0 50.0 29.0 26.0 36.0 34.5 21.5
## 37 97.2 75.0 77.2 91.3 49.5 31.0 26.1 36.3 35.1 21.0
## 38 91.5 72.1 79.2 91.0 54.9 29.5 24.5 36.1 37.2 22.9
## 39 91.2 78.8 78.0 93.2 55.8 31.9 27.4 36.4 35.1 23.0
## 40 101.1 77.5 78.0 97.0 55.0 37.7 29.9 38.3 39.6 23.3
## 41 104.3 91.5 93.2 103.9 62.0 36.3 29.0 36.7 39.4 23.1
## 42 110.8 84.9 83.0 102.6 66.4 42.3 30.9 37.0 37.7 22.6
## 43 96.3 79.1 78.3 97.1 60.1 35.5 28.8 36.9 38.2 23.4
## 44 102.7 77.9 77.9 90.7 56.7 35.4 28.3 35.6 35.5 22.9
## 45 103.9 91.7 89.4 101.8 61.0 35.7 29.4 37.7 40.0 22.2
## 46 105.6 86.6 87.3 103.9 63.2 37.8 29.7 39.0 40.2 24.3
## 47 95.8 84.7 84.0 101.4 60.0 35.0 28.5 38.4 37.9 23.2
## 48 111.2 90.3 93.5 108.7 66.9 40.2 32.4 39.2 40.1 25.7
## 49 100.0 79.7 87.1 98.4 61.1 36.3 28.6 34.5 36.1 21.4
## 50 91.6 73.1 75.4 86.5 50.6 30.8 26.1 31.7 33.6 20.3
## 51 108.0 79.8 82.5 94.8 58.3 39.8 29.6 34.2 38.1 21.1
## 52 109.6 81.6 86.5 100.9 61.7 39.5 31.7 38.8 36.5 22.7
## 53 105.7 76.8 83.4 98.0 56.8 37.9 30.9 35.9 38.3 23.4
## 54 109.1 85.9 90.4 100.9 61.3 40.1 30.0 36.8 38.6 21.9
## 55 88.8 73.3 77.9 85.7 46.9 30.5 24.8 31.1 30.5 19.0
## 56 86.1 69.9 67.4 84.1 50.8 31.5 26.6 32.8 36.3 20.0
## 57 91.3 72.7 83.2 91.4 51.2 27.8 26.0 34.8 34.7 21.1
## 58 100.6 82.7 83.5 98.0 55.8 33.1 28.0 37.9 39.1 23.2
## 59 105.5 90.1 89.2 104.5 62.7 36.3 29.6 38.4 42.4 25.3
## 60 97.5 82.9 83.6 95.8 52.6 34.5 27.0 35.2 35.2 21.4
## 61 94.4 77.9 79.0 91.7 57.1 31.2 27.5 36.6 37.5 21.6
## 62 99.6 92.5 96.2 103.4 58.5 34.5 28.4 38.4 38.0 22.4
## 63 98.1 77.8 77.2 90.0 52.4 33.2 26.4 34.2 36.0 21.8
## 64 93.6 72.7 77.3 91.7 51.9 32.1 27.4 33.5 33.8 21.1
## 65 93.4 75.0 79.2 94.0 53.8 34.2 27.9 36.1 36.2 22.0
## 66 92.0 76.0 83.0 93.0 54.5 29.5 26.0 37.0 34.5 22.8
## 67 99.2 82.7 84.2 93.0 56.6 32.4 27.6 35.8 36.3 21.8
## 68 97.6 80.0 85.7 97.4 57.8 33.8 28.6 36.2 37.4 22.0
## 69 108.8 107.1 107.2 108.3 67.0 39.6 30.6 40.0 39.6 24.6
## 70 91.9 76.2 78.1 90.0 52.0 30.7 25.8 34.8 32.6 21.0
## 71 105.2 90.2 88.6 100.2 60.8 35.7 29.4 39.2 39.1 24.5
## 72 98.3 89.4 87.4 97.7 54.8 31.0 26.0 36.4 35.6 21.6
## 73 92.5 80.9 78.5 96.0 59.0 31.5 26.3 36.1 39.0 21.2
## 74 92.5 73.5 76.4 92.0 53.1 30.6 27.1 36.0 36.0 23.8
## 75 101.6 70.9 76.7 95.3 56.0 36.0 28.6 36.0 34.0 22.0
## 76 94.6 76.1 78.0 86.3 52.4 28.6 23.9 34.5 37.9 22.7
## 77 92.5 81.0 85.2 92.5 54.7 32.3 26.8 35.8 37.6 21.1
## 78 88.2 72.0 72.0 85.5 50.2 28.6 24.8 34.9 35.1 20.1
## 79 91.0 76.8 80.0 94.5 54.6 33.2 28.0 37.5 35.6 22.1
## 80 106.0 86.0 92.0 103.0 60.6 34.0 29.8 38.8 39.5 23.6
## 81 115.0 98.5 106.6 116.5 67.8 35.8 27.2 38.0 41.2 23.3
## 82 100.0 79.0 82.5 98.5 62.1 34.0 28.8 39.6 40.8 25.9
## 83 94.7 77.5 80.5 92.0 54.2 30.9 26.6 36.5 35.8 21.3
## 84 92.5 75.2 80.2 91.6 49.6 29.2 26.1 36.2 35.7 22.1
## 85 96.7 82.0 82.2 92.7 54.6 32.0 27.1 35.6 36.4 20.7
## 86 97.4 79.6 80.8 95.0 54.2 32.6 27.4 36.5 38.0 21.6
## 87 106.7 75.2 77.8 94.5 57.4 36.7 29.9 38.1 36.0 22.6
## 88 106.2 88.6 88.3 100.5 63.4 36.9 29.4 38.4 38.6 23.1
## 89 103.6 81.5 83.3 91.8 55.0 33.0 27.8 35.4 36.5 21.9
## 90 98.3 79.9 82.4 87.5 54.4 33.5 27.3 36.8 37.9 22.3
## 91 87.8 73.5 77.5 94.9 53.5 34.3 28.5 36.5 35.2 22.0
## 92 99.8 80.3 80.8 93.0 55.4 33.3 28.0 36.0 37.8 20.3
## 93 104.6 81.5 85.0 92.0 54.1 33.0 28.0 35.1 35.2 21.1
## 94 86.5 74.0 76.5 91.3 53.5 30.5 26.1 36.6 38.6 21.2
## 95 110.0 104.0 99.0 111.7 63.2 37.5 29.0 41.2 39.3 24.6
## 96 93.2 76.2 83.8 92.8 55.2 31.2 26.2 36.8 37.7 22.7
## 97 90.0 76.5 77.7 91.2 54.2 33.1 27.2 35.5 35.3 21.5
## 98 98.4 81.0 80.5 96.2 56.0 32.0 27.4 37.0 35.5 24.0
## 99 107.2 88.8 86.8 100.0 61.0 34.6 27.9 38.0 39.4 23.2
## 100 108.3 94.0 98.0 108.2 66.8 35.6 27.3 39.5 43.0 25.3
## 101 105.7 83.4 86.5 101.1 61.3 34.7 29.4 39.4 41.8 24.0
## 102 88.5 77.0 79.0 93.0 51.7 33.5 27.9 38.4 38.5 22.5
## 103 79.3 75.4 78.0 88.6 50.0 25.6 22.7 33.8 32.5 21.2
## 104 90.9 80.3 80.8 92.8 53.9 32.5 28.0 36.5 35.0 21.0
## 105 90.2 68.0 67.0 81.5 49.5 27.0 23.6 34.0 34.5 20.9
## 106 91.6 80.6 78.0 91.3 55.0 30.7 25.3 35.5 34.0 20.8
## 107 105.2 88.6 94.7 94.7 58.3 36.9 28.8 40.3 39.7 26.3
## 108 97.0 81.1 88.2 93.9 53.5 33.7 28.6 35.0 37.3 23.1
## 109 85.3 70.8 84.9 89.4 55.8 28.7 25.5 38.5 34.2 21.3
## 110 99.6 73.3 82.1 89.3 55.4 36.3 32.5 34.3 34.3 22.3
## 111 94.3 75.9 79.1 92.6 54.4 33.2 27.9 34.8 35.5 23.0
## 112 111.8 86.2 93.5 96.3 59.1 36.3 28.0 38.3 34.7 23.0
## 113 94.3 75.0 82.2 88.0 53.8 36.3 28.9 34.5 33.5 23.0
## 114 106.1 101.0 99.7 105.5 60.2 38.6 30.3 39.5 39.4 25.6
## 115 102.0 90.0 92.3 102.3 60.0 34.6 29.7 38.2 38.3 23.7
## 116 94.8 75.0 79.6 91.6 49.4 30.0 26.5 31.7 30.2 16.4
## 117 102.9 75.9 77.0 93.4 55.0 35.2 28.7 37.0 37.7 24.5
## 118 115.8 96.0 95.9 103.6 62.2 38.2 30.1 41.2 39.4 25.1
## 119 105.4 84.0 90.4 94.8 57.6 38.7 30.2 38.6 38.2 22.8
## 120 87.1 67.1 80.4 85.9 46.8 30.3 25.4 32.7 32.1 20.0
## 121 104.1 82.5 90.1 98.4 57.7 37.9 31.6 37.8 38.3 24.6
## 122 95.8 83.7 84.2 98.4 56.2 33.7 28.0 38.0 39.6 25.8
## 123 98.6 76.7 85.8 93.3 56.0 35.7 27.6 34.7 34.6 20.6
## 124 118.7 105.2 105.0 115.5 69.9 39.4 32.1 42.2 47.7 27.0
## 125 100.9 90.6 93.3 97.7 58.0 34.8 28.0 34.1 35.8 22.2
## 126 98.5 85.7 92.9 98.6 55.5 35.3 28.7 39.3 35.9 23.0
## 127 96.9 82.5 90.8 94.9 54.4 32.8 28.7 39.2 37.0 27.5
## 128 110.7 94.7 92.0 101.3 60.1 37.2 30.9 40.5 40.0 24.2
## 129 108.0 105.2 103.4 108.1 60.5 38.0 30.2 36.9 37.7 21.6
## 130 109.0 86.0 90.2 98.0 59.5 40.0 31.2 38.3 39.0 25.8
## 131 104.2 90.9 92.7 100.2 51.8 30.1 26.8 38.1 36.4 23.2
## 132 100.5 92.4 92.4 97.0 50.9 32.9 29.0 37.7 37.7 23.4
## 133 105.7 96.5 98.2 97.4 54.3 31.9 28.5 37.7 39.3 24.5
## 134 112.4 98.4 101.5 107.9 67.4 39.2 30.5 42.6 40.7 25.3
## 135 96.2 76.7 83.5 93.9 50.4 32.1 27.7 36.1 32.9 23.2
## 136 97.5 94.8 98.2 98.6 48.3 31.1 27.0 37.7 36.8 24.6
## 137 90.9 80.1 79.8 91.3 56.2 32.9 27.2 36.2 33.0 23.0
## 138 108.4 97.4 103.7 105.3 55.6 36.6 28.4 38.2 36.6 22.9
## 139 94.3 73.7 74.5 88.2 52.3 29.6 26.2 35.2 36.2 21.2
## 140 109.1 76.1 90.1 93.3 51.7 37.0 30.6 36.8 37.7 23.6
## 141 115.0 95.6 101.9 107.9 64.6 37.1 30.0 41.8 39.6 24.7
## 142 104.4 101.0 98.9 103.3 54.4 38.1 29.8 39.7 41.8 25.0
## 143 100.1 84.5 84.5 94.4 54.7 33.9 28.6 38.5 37.6 25.0
## 144 108.4 98.0 101.8 101.5 56.9 38.2 29.9 37.7 39.2 24.9
## 145 107.3 101.6 103.8 110.0 57.8 34.9 28.9 40.3 40.0 23.7
## 146 101.8 87.8 90.2 98.4 55.6 33.1 28.4 38.2 37.7 24.5
## 147 94.5 80.0 85.0 95.0 52.0 31.5 26.5 36.9 36.4 22.9
## 148 91.7 81.8 82.9 98.3 56.3 31.0 25.7 35.0 33.0 22.0
## 149 95.9 84.4 86.8 99.0 55.0 30.5 26.4 36.1 38.4 21.3
## 150 110.5 85.0 83.5 95.7 59.0 39.2 29.9 37.9 37.7 23.8
## 151 104.0 90.0 86.0 96.0 52.5 33.5 29.1 36.0 36.9 23.0
## 152 86.8 72.9 73.4 89.5 51.0 29.8 24.8 32.6 33.1 22.1
## 153 106.7 81.0 80.2 93.7 54.8 35.5 30.6 36.9 37.3 22.7
## 154 102.5 86.5 89.0 97.0 57.0 34.0 28.4 38.0 37.0 22.5
## 155 103.0 93.9 98.6 103.6 60.5 34.4 28.5 40.9 40.8 24.6
## 156 95.0 77.0 78.0 93.0 52.0 32.6 28.4 34.4 34.4 20.0
## 157 99.0 75.0 75.0 90.0 50.6 32.0 27.3 33.8 34.0 22.0
## 158 89.7 80.6 80.8 90.0 55.5 28.9 25.0 34.6 37.4 23.0
## 159 111.5 100.5 107.3 109.5 61.8 37.4 31.6 41.0 39.7 25.4
## 160 94.1 81.2 84.0 91.6 51.5 33.0 27.0 35.2 35.5 23.1
## 161 118.3 103.4 106.2 108.5 60.5 35.4 29.7 42.3 40.8 24.8
## 162 106.5 90.3 101.1 101.6 57.2 35.4 28.6 40.4 37.8 24.9
## 163 110.4 98.0 98.0 99.6 56.7 36.4 29.2 40.9 42.1 26.1
## 164 102.3 86.5 87.7 91.9 55.0 35.0 28.9 38.3 37.8 24.0
## 165 98.5 77.9 87.3 90.8 50.8 35.0 28.4 35.5 35.0 21.0
## 166 111.6 89.1 95.1 104.8 62.7 37.9 31.2 41.1 41.2 27.7
## 167 106.7 93.9 111.8 111.4 62.8 36.2 29.7 42.8 39.3 23.5
## 168 110.4 85.3 82.9 96.5 57.0 39.0 29.8 36.8 36.0 21.6
## 169 114.0 98.5 103.8 108.1 61.3 37.2 31.4 41.9 42.1 26.4
## 170 101.8 79.5 90.1 95.3 54.8 34.2 28.5 36.6 36.2 22.8
## 171 109.6 94.9 94.7 104.3 59.0 35.9 27.8 37.7 36.8 23.2
## 172 100.7 76.5 87.2 96.3 54.2 33.8 27.7 36.4 38.2 23.8
## 173 104.3 88.4 89.6 98.8 54.8 35.5 29.7 37.7 37.0 23.7
## 174 104.2 84.2 84.0 93.2 55.0 33.0 25.4 35.6 36.4 22.8
## 175 107.4 87.6 89.4 106.7 60.9 38.3 31.2 39.0 42.6 25.8
## 176 101.0 83.7 91.1 99.9 56.8 33.5 27.7 38.7 41.8 29.3
## 177 103.0 92.1 91.3 103.8 56.6 33.3 27.7 37.1 37.4 22.6
## 178 107.2 89.9 94.7 107.1 59.2 35.3 26.9 36.6 32.3 22.0
## 179 99.0 88.7 91.0 100.0 57.5 34.0 28.3 40.9 38.8 26.4
## 180 100.3 83.9 89.4 103.9 59.8 36.1 29.4 37.0 36.5 24.3
## 181 100.2 79.5 88.7 95.3 52.5 34.6 25.8 35.6 35.1 21.8
## 182 99.8 84.5 92.6 99.5 59.2 34.3 29.0 36.5 38.5 24.5
## 183 107.5 89.2 88.4 107.0 56.9 35.6 28.5 37.0 37.6 23.0
## 184 110.1 90.7 91.9 101.7 58.0 36.8 29.0 36.9 38.9 24.2
## 185 107.0 88.8 97.5 103.8 61.0 36.7 28.6 38.4 39.5 24.4
## 186 105.6 103.6 100.7 100.6 55.3 33.6 26.9 37.8 37.9 23.9
## 187 103.6 98.5 99.9 103.6 57.5 33.7 29.0 38.7 36.7 24.3
## 188 97.1 82.9 88.1 91.2 51.7 30.7 25.7 33.9 33.4 21.2
## 189 109.8 90.5 92.3 95.2 52.4 35.8 28.7 32.5 36.5 23.7
## 190 103.3 84.5 94.5 98.2 53.7 32.5 27.8 36.0 36.3 22.0
## 191 103.7 86.0 93.8 97.1 53.1 33.9 27.3 35.7 36.6 22.6
## 192 108.5 84.2 88.9 97.5 58.8 36.6 29.9 34.2 34.8 22.0
## 193 97.8 85.7 89.5 94.9 51.7 32.2 26.4 34.4 32.6 22.0
## 194 112.7 112.1 105.9 106.3 56.9 35.7 27.8 37.3 36.6 22.7
## 195 111.4 99.7 102.9 105.8 57.8 36.5 30.5 39.0 41.2 25.7
## 196 95.1 84.7 92.9 96.7 54.6 32.8 25.3 36.6 35.0 23.5
## 197 100.2 80.3 92.4 96.4 53.8 35.7 29.2 38.4 37.0 25.6
## 198 106.3 98.6 111.7 118.7 70.0 37.1 27.8 37.5 39.2 25.7
## 199 109.5 90.0 96.2 104.3 63.5 39.4 29.9 37.4 37.3 24.3
## 200 106.3 86.6 93.9 95.9 53.6 34.4 28.6 35.0 34.1 21.7
## 201 91.5 80.2 85.7 89.2 48.5 28.7 25.0 35.4 32.3 23.0
## 202 104.9 109.2 104.4 101.7 56.4 34.0 29.2 39.3 38.5 24.3
## 203 109.6 88.4 92.0 95.1 52.5 39.4 29.8 34.5 34.0 22.0
## 204 102.5 81.0 84.5 105.0 56.0 31.5 26.5 38.5 36.9 21.3
## 205 101.2 88.8 90.8 101.3 62.5 35.2 28.9 40.6 39.2 23.0
## 206 98.7 78.1 78.6 92.0 56.5 35.7 29.2 36.4 37.0 22.0
## 207 96.0 81.5 80.5 89.5 52.0 30.3 25.0 36.0 35.0 22.4
## 208 104.2 87.6 89.6 100.5 60.7 36.5 31.1 40.7 38.4 22.9
## 209 103.0 92.5 88.5 94.0 55.0 36.0 28.0 36.5 37.0 21.8
## 210 107.0 97.0 95.5 104.5 56.6 34.4 28.9 40.0 38.5 24.0
## 211 101.0 82.0 82.0 98.0 59.0 35.4 29.0 38.0 42.0 23.6
## 212 112.1 99.5 97.8 107.4 60.5 35.5 28.8 42.9 38.7 25.7
## 213 103.4 93.8 92.7 112.2 66.2 34.8 30.1 45.7 43.6 26.9
## 214 100.3 79.1 80.4 94.3 51.0 32.6 27.2 36.1 32.7 22.5
## 215 95.7 85.8 94.7 106.8 60.6 33.6 27.3 37.5 41.8 26.2
## 216 108.0 90.8 92.4 100.3 56.5 36.8 29.3 37.5 36.3 23.4
## 217 101.0 85.4 86.9 101.8 57.0 34.0 27.1 39.4 37.1 23.7
## 218 98.6 91.6 102.1 106.7 57.8 32.3 27.9 41.8 41.5 27.7
## 219 101.6 79.7 82.0 98.4 58.1 36.5 31.0 38.0 38.1 25.3
## 220 99.0 86.1 90.8 101.3 56.0 33.5 28.3 37.7 38.3 25.2
## 221 116.7 113.2 102.9 107.9 57.7 37.4 28.9 37.8 37.4 24.1
## 222 105.0 79.5 85.8 92.7 51.8 36.2 27.0 33.9 28.9 20.3
## 223 95.1 85.4 84.1 94.3 52.7 31.2 25.9 37.4 34.4 24.5
## 224 106.7 97.9 94.7 104.6 60.8 36.2 28.7 37.7 39.4 22.6
## 225 116.6 94.7 93.1 103.3 58.0 42.3 31.9 39.9 39.6 25.5
## 226 103.5 86.1 90.5 96.7 55.2 34.5 27.7 37.3 34.8 22.5
## 227 90.4 84.9 83.7 97.9 51.8 28.0 25.2 37.5 36.0 21.3
## 228 107.5 92.2 88.6 97.5 53.7 34.3 27.6 36.0 37.5 23.3
## 229 100.8 83.7 82.5 97.7 53.3 32.5 27.1 35.4 37.0 22.7
## 230 104.2 97.8 93.6 102.5 58.0 35.8 29.4 39.0 38.1 23.0
## 231 104.9 98.6 99.2 103.3 55.3 35.0 29.3 35.9 36.0 23.5
## 232 112.8 89.5 96.9 100.9 54.9 38.5 28.7 35.9 33.6 22.1
## 233 95.7 82.9 89.6 94.8 51.9 32.2 25.3 33.4 32.8 21.4
## 234 104.9 90.1 90.8 96.6 55.0 32.9 26.5 35.6 37.9 22.5
## 235 109.1 78.9 91.0 98.1 55.7 38.5 30.1 37.2 36.8 23.4
## 236 105.4 80.7 87.4 95.5 56.8 38.3 28.6 35.0 34.3 23.3
## 237 104.3 94.3 99.4 100.4 59.1 35.0 26.7 35.5 35.9 22.6
## 238 100.5 70.2 79.3 92.0 51.7 32.1 26.7 33.2 34.9 23.7
## 239 111.8 83.6 92.7 101.5 59.5 40.4 31.7 36.7 38.3 25.5
## 240 109.5 91.9 96.5 103.3 57.7 36.5 29.1 34.6 38.8 25.1
## 241 101.2 71.8 82.3 87.6 50.1 34.2 29.2 34.1 33.4 23.1
## 242 103.3 85.0 90.8 97.9 55.2 35.2 29.4 34.9 37.3 23.5
## 243 101.6 85.7 91.0 95.9 50.9 34.0 28.4 35.0 34.3 21.1
## 244 103.1 96.5 99.0 111.8 62.3 34.8 27.5 41.7 37.0 24.3
## 245 104.6 82.4 85.7 99.9 63.3 38.6 32.0 38.4 39.8 25.4
## 246 104.3 86.3 87.8 103.3 59.7 36.4 30.4 39.3 42.0 27.7
## 247 95.9 83.2 88.0 100.6 57.8 34.0 28.2 36.3 39.6 25.2
## wri.gi age wgt hgt sex
## 1 16.5 21 65.6 174.0 1
## 2 17.0 23 71.8 175.3 1
## 3 16.9 28 80.7 193.5 1
## 4 16.6 23 72.6 186.5 1
## 5 18.0 22 78.8 187.2 1
## 6 16.9 21 74.8 181.5 1
## 7 18.8 26 86.4 184.0 1
## 8 18.0 27 78.4 184.5 1
## 9 16.5 23 62.0 175.0 1
## 10 16.9 21 81.6 184.0 1
## 11 16.2 23 76.6 180.0 1
## 12 18.2 22 83.6 177.8 1
## 13 18.0 20 90.0 192.0 1
## 14 16.6 26 74.6 176.0 1
## 15 16.5 23 71.0 174.0 1
## 16 17.5 22 79.6 184.0 1
## 17 17.8 30 93.8 192.7 1
## 18 17.1 22 70.0 171.5 1
## 19 18.5 29 72.4 173.0 1
## 20 18.8 22 85.9 176.0 1
## 21 17.3 22 78.8 176.0 1
## 22 18.0 20 77.8 180.5 1
## 23 16.0 22 66.2 172.7 1
## 24 17.0 24 86.4 176.0 1
## 25 18.2 26 81.8 173.5 1
## 26 19.0 24 89.6 178.0 1
## 27 16.7 21 82.8 180.3 1
## 28 17.8 24 76.4 180.3 1
## 29 16.5 23 63.2 164.5 1
## 30 15.6 19 60.9 173.0 1
## 31 16.6 23 74.8 183.5 1
## 32 17.2 25 70.0 175.5 1
## 33 17.0 23 72.4 188.0 1
## 34 17.2 23 84.1 189.2 1
## 35 16.9 23 69.1 172.8 1
## 36 17.0 20 59.5 170.0 1
## 37 17.0 22 67.2 182.0 1
## 38 16.0 24 61.3 170.0 1
## 39 16.8 22 68.6 177.8 1
## 40 18.7 24 80.1 184.2 1
## 41 17.6 21 87.8 186.7 1
## 42 17.5 23 84.7 171.4 1
## 43 16.7 24 73.4 172.7 1
## 44 17.0 35 72.1 175.3 1
## 45 17.9 29 82.6 180.3 1
## 46 18.9 25 88.7 182.9 1
## 47 16.8 23 84.1 188.0 1
## 48 17.7 20 94.1 177.2 1
## 49 16.3 25 74.9 172.1 1
## 50 15.8 29 59.1 167.0 1
## 51 16.9 23 75.6 169.5 1
## 52 17.9 23 86.2 174.0 1
## 53 17.3 36 75.3 172.7 1
## 54 16.4 25 87.1 182.2 1
## 55 15.0 24 55.2 164.1 1
## 56 15.8 20 57.0 163.0 1
## 57 15.3 52 61.4 171.5 1
## 58 17.7 50 76.8 184.2 1
## 59 17.5 46 86.8 174.0 1
## 60 16.5 51 72.2 174.0 1
## 61 16.1 28 71.6 177.0 1
## 62 17.2 48 84.8 186.0 1
## 63 17.5 35 68.2 167.0 1
## 64 16.9 23 66.1 171.8 1
## 65 17.5 23 72.0 182.0 1
## 66 17.4 62 64.6 167.0 1
## 67 16.7 21 74.8 177.8 1
## 68 17.2 26 70.0 164.5 1
## 69 17.7 33 101.6 192.0 1
## 70 16.1 36 63.2 175.5 1
## 71 17.9 41 79.1 171.2 1
## 72 16.6 40 78.9 181.6 1
## 73 15.6 27 67.7 167.4 1
## 74 17.5 27 66.0 181.1 1
## 75 17.0 23 68.2 177.0 1
## 76 15.8 31 63.9 174.5 1
## 77 15.8 26 72.0 177.5 1
## 78 15.4 23 56.8 170.5 1
## 79 16.3 24 74.5 182.4 1
## 80 18.0 24 90.9 197.1 1
## 81 16.0 34 93.0 180.1 1
## 82 18.0 21 80.9 175.5 1
## 83 16.5 25 72.7 180.6 1
## 84 16.7 34 68.0 184.4 1
## 85 16.2 31 70.9 175.5 1
## 86 16.6 40 72.5 180.6 1
## 87 17.3 21 72.5 177.0 1
## 88 17.3 33 83.4 177.1 1
## 89 16.4 25 75.5 181.6 1
## 90 16.6 29 73.0 176.5 1
## 91 17.0 27 70.2 175.0 1
## 92 16.5 44 73.4 174.0 1
## 93 16.3 26 70.5 165.1 1
## 94 16.0 22 68.9 177.0 1
## 95 18.6 37 102.3 192.0 1
## 96 16.2 38 68.4 176.5 1
## 97 16.2 20 65.9 169.4 1
## 98 16.5 21 75.7 182.1 1
## 99 17.0 24 84.5 179.8 1
## 100 17.7 45 87.7 175.3 1
## 101 17.8 25 86.4 184.9 1
## 102 17.5 22 73.2 177.3 1
## 103 14.6 29 53.9 167.4 1
## 104 16.4 37 72.0 178.1 1
## 105 16.0 20 55.5 168.9 1
## 106 16.4 20 58.4 157.2 1
## 107 18.1 32 83.2 180.3 1
## 108 16.7 23 72.7 170.2 1
## 109 15.6 25 64.1 177.8 1
## 110 18.4 27 72.3 172.7 1
## 111 16.3 21 65.0 165.1 1
## 112 16.1 27 86.4 186.7 1
## 113 17.1 25 65.0 165.1 1
## 114 18.3 38 88.6 174.0 1
## 115 18.0 44 84.1 175.3 1
## 116 16.1 27 66.8 185.4 1
## 117 17.3 37 75.5 177.8 1
## 118 17.7 28 93.2 180.3 1
## 119 18.2 33 82.7 180.3 1
## 120 15.3 25 58.0 177.8 1
## 121 18.1 21 79.5 177.8 1
## 122 17.6 30 78.6 177.8 1
## 123 16.0 26 71.8 177.8 1
## 124 19.2 27 116.4 177.8 1
## 125 16.3 33 72.2 163.8 1
## 126 17.4 29 83.6 188.0 1
## 127 17.9 27 85.5 198.1 1
## 128 17.6 34 90.9 175.3 1
## 129 18.3 42 85.9 166.4 1
## 130 19.5 29 89.1 190.5 1
## 131 16.3 41 75.0 166.4 1
## 132 17.0 43 77.7 177.8 1
## 133 17.1 43 86.4 179.7 1
## 134 17.5 29 90.9 172.7 1
## 135 17.0 27 73.6 190.5 1
## 136 18.4 62 76.4 185.4 1
## 137 16.8 33 69.1 168.9 1
## 138 18.1 45 84.5 167.6 1
## 139 16.2 30 64.5 175.3 1
## 140 18.5 20 69.1 170.2 1
## 141 18.2 22 108.6 190.5 1
## 142 19.6 51 86.4 177.8 1
## 143 17.7 34 80.9 190.5 1
## 144 17.6 44 87.7 177.8 1
## 145 18.1 46 94.5 184.2 1
## 146 17.1 34 80.2 176.5 1
## 147 17.0 32 72.0 177.8 1
## 148 15.5 28 71.4 180.3 1
## 149 16.4 31 72.7 171.4 1
## 150 17.1 29 84.1 172.7 1
## 151 18.0 42 76.8 172.7 1
## 152 16.3 29 63.6 177.8 1
## 153 16.8 31 80.9 177.8 1
## 154 17.4 30 80.9 182.9 1
## 155 17.1 27 85.5 170.2 1
## 156 16.5 25 68.6 167.6 1
## 157 17.0 24 67.7 175.3 1
## 158 16.4 33 66.4 165.1 1
## 159 18.4 45 102.3 185.4 1
## 160 16.3 37 70.5 181.6 1
## 161 17.1 44 95.9 172.7 1
## 162 17.9 34 84.1 190.5 1
## 163 19.5 55 87.3 179.1 1
## 164 17.3 43 71.8 175.3 1
## 165 16.6 24 65.9 170.2 1
## 166 18.1 22 95.9 193.0 1
## 167 16.8 38 91.4 171.4 1
## 168 17.3 24 81.8 177.8 1
## 169 17.9 29 96.8 177.8 1
## 170 17.3 25 69.1 167.6 1
## 171 16.5 37 82.7 167.6 1
## 172 18.2 30 75.5 180.3 1
## 173 18.3 26 79.5 182.9 1
## 174 15.9 35 73.6 176.5 1
## 175 18.8 29 91.8 186.7 1
## 176 18.0 30 84.1 188.0 1
## 177 17.1 37 85.9 188.0 1
## 178 17.1 34 81.8 177.8 1
## 179 18.1 28 82.5 174.0 1
## 180 18.7 27 80.5 177.8 1
## 181 16.3 32 70.0 171.4 1
## 182 17.3 28 81.8 185.4 1
## 183 17.5 22 84.1 185.4 1
## 184 17.9 44 90.5 188.0 1
## 185 16.8 25 91.4 188.0 1
## 186 17.1 49 89.1 182.9 1
## 187 17.7 54 85.0 176.5 1
## 188 16.7 49 69.1 175.3 1
## 189 17.5 60 73.6 175.3 1
## 190 17.7 42 80.5 188.0 1
## 191 17.5 52 82.7 188.0 1
## 192 18.1 23 86.4 175.3 1
## 193 16.4 33 67.7 170.5 1
## 194 16.4 46 92.7 179.1 1
## 195 18.8 43 93.6 177.8 1
## 196 17.1 56 70.9 175.3 1
## 197 17.9 21 75.0 182.9 1
## 198 15.9 18 93.2 170.8 1
## 199 17.2 21 93.2 188.0 1
## 200 17.1 45 77.7 180.3 1
## 201 16.2 22 61.4 177.8 1
## 202 17.4 55 94.1 185.4 1
## 203 17.0 42 75.0 168.9 1
## 204 16.6 29 83.6 185.4 1
## 205 17.5 40 85.5 180.3 1
## 206 17.2 24 73.9 174.0 1
## 207 16.7 62 66.8 167.6 1
## 208 17.9 26 87.3 182.9 1
## 209 17.5 35 72.3 160.0 1
## 210 17.0 37 88.6 180.3 1
## 211 17.5 34 75.5 167.6 1
## 212 17.1 25 101.4 186.7 1
## 213 17.0 30 91.1 175.3 1
## 214 17.9 32 67.3 175.3 1
## 215 17.8 27 77.7 175.9 1
## 216 16.7 42 81.8 175.3 1
## 217 16.6 44 75.5 179.1 1
## 218 18.1 46 84.5 181.6 1
## 219 17.7 19 76.6 177.8 1
## 220 17.4 43 85.0 182.9 1
## 221 17.1 28 102.5 177.8 1
## 222 15.8 39 77.3 184.2 1
## 223 17.1 30 71.8 179.1 1
## 224 17.5 36 87.9 176.5 1
## 225 18.9 48 94.3 188.0 1
## 226 16.4 48 70.9 174.0 1
## 227 15.1 53 64.5 167.6 1
## 228 16.7 45 77.3 170.2 1
## 229 16.6 39 72.3 167.6 1
## 230 17.0 43 87.3 188.0 1
## 231 18.1 65 80.0 174.0 1
## 232 17.1 45 82.3 176.5 1
## 233 16.3 37 73.6 180.3 1
## 234 17.8 55 74.1 167.6 1
## 235 19.6 33 85.9 188.0 1
## 236 17.3 25 73.2 180.3 1
## 237 17.3 35 76.3 167.6 1
## 238 18.4 28 65.9 183.0 1
## 239 19.4 26 90.9 183.0 1
## 240 18.9 43 89.1 179.1 1
## 241 18.3 30 62.3 170.2 1
## 242 17.3 26 82.7 177.8 1
## 243 16.3 51 79.1 179.1 1
## 244 16.7 30 98.2 190.5 1
## 245 18.1 24 84.1 177.8 1
## 246 18.4 35 83.2 180.3 1
## 247 17.0 37 83.2 180.3 1Example 1: histogram of men’s heights and histogram of women’s heights.
# men's heights
hist(mdims$hgt, main = "Histogram of Men's Heights", xlab = "Height in cm", las = 1)
# women's heights
hist(fdims$hgt, main = "Histogram of Women's Heights", xlab = "Height in cm", las = 1)
Comparison of height histograms: The range between men’s heights overlaps the range for women’s heights with women being on the lower end and men being on the higher end. What I mean by women being on the lower end is women having a minimum height of 150 cm while men have a minimum of 160. Women also have a maximum height of 180 cm while men have a maximum of around 200 cm. Men have a peak height around 180 cm with the second and third highest peaks being 185 and 175 respectively. The highest peak for women is around 170 with the second and third highest being 165 and 160 respectively. The frequency of heights between 160 and 170 for women seem more evenly distributed while men have a dramatic spike at 180 and a drop at either side of that peak.
Mean height and standard deviation for women with histogram
fhgtmean <- mean(fdims$hgt)
fhgtsd <- sd(fdims$hgt)
hist(fdims$hgt, main = "Density Histogram of Female Heights", xlab = "Height in cm", las = 1, probability = TRUE)
x <- 140:190
y <- dnorm(x = x, mean = fhgtmean, sd = fhgtsd)
lines(x = x, y = y, col = "blue")
Exercise 2: Is there a nearly normal distribution? Yes I do think there is nearly a normal distrubution. It is just a bit left skewed but because it sits under the bell it appears more like a normal distribution than left skewed.
Q-Q plot of heights
qqnorm(fdims$hgt)
qqline(fdims$hgt)
Exercise 3: Create simulation of data from a normal distribution and plot it
sim_norm <- rnorm(n = length(fdims$hgt), mean = fhgtmean, sd = fhgtsd)
qqnorm(sim_norm)
qqline(sim_norm)
The simulated plot has a greater number of plot points that land on the line than the plot for fdims. The simulated plot also has fewer outliers at the top of the line. The similarities between the two plots lie in the bottom outliers. Both plot graph have greater outliers in the bottom with the plots landing above the line.
qqnormsim(fdims$hgt)
Exercise 4 The normal probability plot for fdims is similar but falls on the line less than the plots for the simulated data. The simulated plot has more plots that land on the line making the plot appear to have one solid black line, while the fdims plot has a little variation. This variation gives it less of a straight line. However, there are enough plots that land on or close to the line for me to say female heights are nearly normal.
Exercise 5: Do female weights appear to come from a normal distribution?
Create mean and sd for female weight
fwgtmean <- mean(fdims$wgt)
fwgtsd <- sd(fdims$wgt)Histogram of female weight
hist(fdims$wgt, probability = TRUE)
x <- 40:110
y <- dnorm(x = x, mean = fwgtmean, sd = fwgtsd)
lines(x = x, y = y, col = "blue")
Evaluating normal distribution of weight
qqnorm(fdims$wgt)
qqline(fdims$wgt)
Simulation of normal weight distribution
simwgt_norm <- rnorm(n = length(fdims$wgt), mean = fwgtmean, sd = fwgtsd)
qqnorm(simwgt_norm)
qqline(simwgt_norm)
qqnormsim(fdims$wgt)
After following the same steps for female weight, it appears that the weight is not a normal distribution. In the histogram the bars and bell both skew to the left, but the bars are further to the left than the bell. Also the peak bar in the histogram is further to the left than the peak of the bell. When comparing the plot of weight to the plot of the simulation, we see that the simulation is similar to the height simulation, most of the plots are on the line. When you look at the plot of the weight, the plots curve upward more on each end so less plot points are on the line.
Normal Probabilities: calculating the Z score
1 - pnorm(q = 182, mean = fhgtmean, sd = fhgtsd)## [1] 0.004434387sum(fdims$hgt > 182) / length(fdims$hgt)## [1] 0.003846154Exercise 6: Probability a female’s height is 70cm
1 - pnorm(q = 70, mean = fhgtmean, sd = fhgtsd)## [1] 1sum(fdims$hgt > 70) / length(fdims$hgt)## [1] 1Probability a female’s weight is 80
1 - pnorm(q = 80, mean = fwgtmean, sd = fwgtsd)## [1] 0.02182199sum(fdims$wgt > 80) / length(fdims$wgt)## [1] 0.04230769The variable height had a closer agreement in the two methods. The result was exactly the same when looking at the probability that a female was 182 cm while the probability for weight is higher using the empirical distribution.
On you own: 1a. The histogram for female biiliac diameter belongs to Plot B
qqnorm(fdims$bii.di)
qqline(fdims$bii.di)
1b. The histogram for female elbow diameter belongs to plot C
qqnorm(fdims$elb.di)
qqline(fdims$elb.di)
1c. The histogram for general age belongs to plot D
qqnorm(fdims$age)
qqline(fdims$age)
1d. The histogram for female chest depth belongs to plot A
qqnorm(fdims$che.de)
qqline(fdims$che.de)
The elbow and age data has a stepwise pattern possibly because the numbers are gradually increasing (in the case of the elbows) and gradually decreasing (in the case of the age).
Normal probability plot for female knee diameter. The data for this variable is left skewed. It easier to see this if we view the data using a histogram. The bars peak around 18-19 in the histogram but the range is from 16 to 24.
qqnorm(fdims$kne.di)
qqline(fdims$kne.di)
hist(fdims$kne.di)