Please answer questions 4 and 5 on the on your own tap

4. As you can see, normal probability plots can be used both to assess normality   and visualize skewness. Make a normal probability plot for female knee   diameter (kne.di). Based on   this normal probability plot, is this variable left skewed, symmetric, or   right skewed? Use a histogram and descriptive statistics to confirm your   findings. Answer using complete sentences.

5. Using   the sample statistics in the Excel NORM.DIST function, compute the following   for the female population. State the formula you entered in Excel, be sure   this is shown on what you submit.

5.1) Probability of randomly   selecting a female whose knee diameter is less than 18.1, P(x<18.1) = ?

5.2)   Probability of randomly selecting a female whose knee diameter is greater   than 16.8, P(x>16.8) = ?

bia.di
bii.di
42.9
43.7
40.1
44.3
42.5
43.3
43.5
44.4
43.5
42
40.3
43.7
47.4
40.3
41
45
39.9
43
43.1
43.6
42
43.8
42.3
42.7
44.8
46
45.4
40.5
39.4
40.2
44.2
41
44
41.6
41
41.5
41.1
38.8
36.2
42.1
40.3
41.7
37.8
39.2
41.5
42.5
bit.di
26
28.5
28.2
29.9
29.9
27
30
29.8
26.5
28
29
29
29.6
27.5
26.8
27
30
26.5
28.6
29.3
27.5
28
26.4
29.9
27.8
30.1
31.8
28.3
25.5
27.2
30.3
23.6
31
32
25.1
24.5
27.8
27.2
27.5
27.5
29.4
27.1
27.1
26.1
30.8
27.8
31.5
33.5
33.3
34
34
31.5
34
33.2
32.1
34
33
31.3
35.7
31.4
32.2
33.2
34.5
30.3
33.4
34.4
30.7
33.3
31.2
35
32.2
34.5
35.2
33.4
30.2
31.7
34.7
30.2
35.3
35.3
31.9
30.5
31.4
31.6
30.4
32.4
32.9
32.6
31.5
30.8
33.3
33.5
che.de
che.di
elb.di
wri.di
kne.di
ank.di
17.7
28
13.1
10.4
18.8
14.1
16.9
30.8
14
11.8
20.6
15.1
20.9
31.7
13.9
10.9
19.7
14.1
18.4
28.2
13.9
11.2
20.9
15
21.5
29.4
15.2
11.6
20.7
14.9
19.6
31.3
14
11.5
18.8
13.9
21.9
31.7
16.1
12.5
20.8
15.6
21.8
28.8
15.1
11.9
21
14.6
15.5
27.5
14.1
11.2
18.9
13.2
22.5
28
15.6
12
21.1
15
20.1
30.3
13.4
10.4
19.4
14.5
20.5
29.7
15
11.7
20.9
16
20.8
31.4
16.1
11.3
21.5
15.4
21.7
28
13.3
10.3
18.8
13.2
21.9
28.6
14.9
10.6
17.8
14
21.7
30.6
13.7
11.1
20.7
14
21
29.4
15.6
11.9
21.2
16
19.3
30
14.8
11.2
19.7
14.7
22.2
29.5
14.9
12.2
20.8
14.8
20.2
32.6
15.4
10.9
20.7
15.5
21.3
32
13.1
11.1
19.2
13.9
20
32
15
11.5
20.4
14.4
18
30.9
14.6
10.8
18.6
13.8
21.8
32.8
14.3
11.2
19.8
14.1
18.3
31.5
15.2
11.6
19.4
14.7
20.2
31.1
16.4
13.3
22.2
14.9
20.2
32.3
14.6
10.5
20.2
15.3
19.2
28.8
14.6
11.1
20.8
14.5
17.6
27.7
13
10.2
18.9
13.2
18.1
26.5
13.3
10.1
18.6
13.2
19.4
30
14.9
11
19.1
15.8
22.9
28
14.3
11.2
18.2
14
19.2
31
15.2
11.4
21.2
15.1
23.6
27
15.5
11.3
20.9
15
20.8
27.9
13.6
10.8
18.8
12.9
17.7
26.7
13.3
10.8
18.6
14
19
31.5
14.5
11.9
18.5
13
18.5
25.5
13.4
10.8
19
14
18.7
28
13.6
10.8
19
15.4
18.2
28
16.2
12
21
16.4
23.7
31.5
14.6
11.3
19.8
15.2
21.6
28
14.1
11.5
19.7
13.8
18.5
27.3
14.6
10.8
19.5
14.9
19.4
29.9
14.3
11.2
20
16
19.4
30.6
14.8
11.3
20.2
16
20.6
30.2
15.9
12.8
22.4
16.3
39.4
43.6
38.9
37.6
39.4
38.5
40.1
40.3
37.6
38.3
39.7
42.2
41.1
40.5
41.5
43.4
43.5
41.3
40.3
36.3
39.9
39.8
43.5
41.2
44
41.8
42.9
38.7
41.4
39.6
40.5
34.1
43.5
44.1
42.2
42.2
43
39.8
37.7
39.6
43.2
44.3
43.3
42.8
41.5
42
41.2
26.1
33.1
24.9
24.4
28.3
26.1
27.8
28
26.6
25.2
28.6
29
30.4
29.3
28.6
32.4
26
27.1
29.5
29.2
28.3
28.8
33.2
26.6
28.4
28.5
27.5
24.6
26.4
27.5
27.5
28.1
28.8
29.2
32.6
30.1
26.5
28.7
29.7
27.9
26.3
28.2
28.2
27.5
30
27.6
27.1
34.4
33.5
28.7
28
30.6
30.8
33.1
32
29.9
30.2
32.1
33.7
35.1
33.7
30.4
36.4
31.6
32.4
33.3
33
32
33
34
30.6
32
31.6
30.3
28.5
32.3
30.2
32.3
30.1
34
35.3
36.6
31.4
31.6
33.3
32.7
33.3
30.5
32.2
33
31.5
33.4
32.2
29.8
20.4
21.6
19.7
18
20.2
20.6
19.2
20.9
17.3
17
19.1
22.5
23.2
19.6
20.8
20.3
19.1
17.5
18.4
20
18.3
19.7
23.9
19.5
22.5
21.6
18.9
18.3
18.6
19.2
19.4
21.8
20.6
23.6
22.4
21.2
20.6
19.3
20.2
20.2
19.7
21.2
19.4
19.2
19.1
19.7
20.1
27.3
33.1
26.8
26.4
28.7
30.8
31.3
31.7
25.6
26.4
27.1
30.4
32.6
29.8
26.9
32.1
30.9
27.6
26.2
29
31.4
28.7
34.3
28
29.7
31.5
29.6
29.8
31.3
28.9
28.8
25.8
29
30.9
34.5
29.7
29.5
29.2
28.8
29.5
30.6
31.8
31.6
31.8
29.4
29.4
31
15.1
15.6
14.2
14.2
15
15.1
15.4
14.8
12.8
13.2
13.4
15.6
15.5
13.8
14.8
15.6
14.3
14.1
14
14.1
13.5
12.4
15.8
13.1
14.9
13.3
12.6
14
14.9
13.5
12.6
12.9
14.3
15.8
14.1
14
13.4
13.5
13.3
12.6
14.4
14.2
13.8
14.1
14.8
13.9
12.9
10.6
12
10.2
10.6
11.5
11.4
11.5
10.6
10
10.4
10
12
11.6
11.7
11.2
12
11.4
10.8
11
11.7
11.4
10.7
12
10.4
10.9
10.3
10.4
11.2
11.5
10.4
10.6
9.9
10.5
12.5
11.1
11.6
10.4
11.6
11.1
10.7
12.3
11.6
11.1
11.1
11
10
11.6
20
20.7
18
17.3
18.4
19.8
20.6
19.4
17
18.8
18.2
19.8
21.5
19.7
20.7
20.8
19.5
20.2
19.4
20.4
18.9
18.5
18.6
19
21
18.9
19.2
18.9
18.9
19.3
18.4
18.6
19.8
20.2
18.2
21.6
18.8
19.5
18.3
18.5
20.2
20
17.8
19.1
19.8
18.7
18.8
15.3
16.5
14.4
13.4
14.4
14.2
15.4
15
13
13
14.8
16.2
15.4
14.4
16.5
16.3
14.6
15.5
14.8
14.3
14.4
13.2
13.2
13.8
14.8
14.3
13.8
13.6
14.6
14.2
14
12.3
14.2
15.2
13.9
14.1
13.6
14.6
13.2
12.9
13.6
14.4
13.2
14.7
13.8
13.8
13.5
43.8
46.2
40.4
40.8
43.9
44.2
41.6
38.1
42
37
41.6
40.1
38.7
37.4
41.7
38
40.5
35.6
43.6
37.6
41.1
42.1
40.5
40.9
43
40.5
41.9
42.1
43.8
42.1
43.4
38.7
39.6
43.4
40.5
40.3
44.2
41.3
39.8
41.3
38.9
41.1
41.5
38.5
39.4
40.9
41.1
29.5
31
28.6
27.1
27
27.9
28
30.1
28
27.3
27.5
19.4
25.2
29.9
28
27.1
24.9
28.5
30.2
24.4
31.7
30.6
28.3
28.5
30.6
27.8
25.4
28.5
29.2
28.5
32
26.8
28.7
30.6
29.7
30.4
30.6
26.8
25.6
29
27.5
25.6
30.6
27.8
29.7
26.1
23
31.2
36
31.4
29.4
33.5
32
35
33.2
33
31.1
32
28
28.8
33.5
32.9
28.3
29.7
29.4
32.4
28.3
34.2
34
32.4
31.3
33.8
31.1
30.2
33.1
32.6
31.7
36.2
31.5
32.4
32.9
31.7
34.2
33.8
32.2
31.3
32.2
32.9
29.9
35.8
31.7
33.1
27.5
29.4
18.2
25
19.8
17.8
22.3
21.6
24.2
21.6
18.1
18.2
18.1
17.1
19.1
22.3
19.4
18.2
19
17.7
21.8
17.7
22.8
22.1
19.4
21.1
23.3
21.8
14.4
20.2
18.7
19.4
23.5
21.4
18.2
21.6
22.1
21.1
22.1
21.4
23.5
25.2
22.5
23.3
21.1
19.7
23
20.2
21.8
29.5
33.1
27.6
29.4
31
32.9
31
31.3
28.4
25
29.5
26.8
25.6
30.8
29.7
25.9
30.2
25.2
33.1
24.7
34
30.6
27.8
29.7
35.3
30.6
26.8
30.6
30.4
28
35.6
27.8
28.3
28.3
32.6
34
32.4
31.1
32
30.8
33.3
25.2
28
26.4
30.4
28
30.6
13.1
14.6
13.9
13.3
13.2
14.3
13.4
14.2
14.3
13.2
13.8
13
13
14.4
14.6
13.8
14.4
14
15.2
12.9
13.8
15
13.4
14.3
15.6
15
12.6
15.6
14.6
14
16.1
13.8
15.2
15
15.2
13.6
15.3
13.6
14
14.4
14.6
14.1
15
13.1
14.2
13.2
15
10.3
12
10.1
10.4
10.4
11
11.2
12.3
11.1
10.5
10.7
10.6
10.2
11.5
11
11
11.8
10.8
11.3
10.8
11.8
11.4
11
11.7
12
11.6
9.8
12.2
11.7
11.3
12.6
10.8
11.8
12
11.3
12
11.5
11
11.2
11
11
10.7
11.8
11
11.6
10.4
10.8
19.1
20.9
20
18.5
19.1
21.1
20.6
19.2
20.2
18.7
19
16.9
17.9
20.5
19.5
18.9
19.5
19.1
19.8
18
19.4
20.2
19
19
21.6
20.4
18.8
19.7
20
19
23
18.2
19.6
20.5
21.2
19.2
20.9
19.1
21.2
19.7
20.5
19
21
18.4
20.4
18.6
19.3
13.2
15.1
13.4
12.8
13.1
14.9
14.4
15.2
15.2
13.4
13.9
12.6
13.5
16.8
15.3
14.8
14.9
15
15.2
14.3
15.4
15.4
14.5
15.6
16.4
15.2
13.6
15.6
15.2
14.4
16.3
13.3
14.8
17.2
15.2
13.8
16.5
15
16.4
15.8
15.3
15.1
15.6
14.8
15
14.8
14.5
43.6
39.8
42.1
41.1
44.2
38.9
40.1
38.7
35.6
40.5
41.1
38.7
38.9
39.4
37.6
39.8
40.3
40.3
43.8
41.1
41.7
45.4
43
41.1
41.1
45.2
39.8
39.6
42.3
40.9
39.8
42.3
42.3
40.5
42.7
43.6
42.5
41.3
41.3
42.3
36.9
40.3
40.1
43.2
45
42.1
40.9
28
29
27.8
27.1
30.4
26.8
28.7
26.8
26.4
26.8
25.4
26.1
27.1
29.7
27.8
25.9
27.3
25.2
30.4
27.8
30.6
30.8
30.8
25.4
29.2
32.2
34.7
28.7
30.2
29
28
27.1
26.8
28.7
28.5
30.8
31.3
30.8
24.7
26.6
25.9
28.5
26.4
31.3
29
29.7
28.7
32.4
34.9
31.7
33.8
36.5
31.5
32.2
31.5
30.8
30.6
32
29.2
30.4
33.1
32.2
31.3
30.4
29.2
34.9
32.9
34.7
35.6
34.7
30.4
31.5
36
34.7
32
34.4
32.2
34.2
31.7
32
30.4
36.7
33.3
33.1
33.3
35.4
33.3
31.7
35.1
32
34
33.3
35.6
33.5
27.5
22.5
20.2
24.9
21.6
20.4
18
18
19.2
21.4
21.6
18.2
20.4
22.3
20.2
19.4
20.4
18.7
24
18
24.9
20.9
22.1
19.2
19.7
22.5
23.5
20.2
25.4
20.2
23.3
17.3
25.4
22.1
23.7
20.4
19.4
22.5
22.5
23.3
19.9
19.2
21.4
23
25.4
23.5
23.7
33.5
28.3
28.7
29.4
31.5
29
29.4
27.8
29.4
32.4
28.7
24.9
28.7
31.5
31.3
29.2
29
28.5
33.3
26.8
32
29.7
32.2
29.9
29.9
33.5
30.2
32.9
32.2
29.2
31.5
29.4
28.7
29.2
30.8
29.7
32
28.3
30.2
28.7
27.3
32
32.6
32.6
30.8
31.3
30.2
14.6
14.3
14.3
14.4
15.4
13.6
15.2
12.9
14.6
15
14.3
13.6
14.8
15.6
14.6
14.3
15
13.2
15.4
14.6
14.9
15.2
16
14.8
14.8
15.8
14.8
14.3
15.2
13.8
14
14.4
15
14.3
15.8
14.3
14.8
13
14.8
14.2
14.8
14.8
14.8
15.7
15.4
14.3
15.8
11.7
11.7
11.5
12.4
11.6
10.8
11.8
10.4
11.5
11.8
12.4
10.4
11.7
12
11
11.2
11.3
10.2
11.6
11.2
10.8
10.8
13.2
10.6
11
11.3
10.6
11.5
10.7
10.4
11
11.6
11.2
11.2
12.9
10.9
11.3
10.5
11.3
11.1
10.6
12
12
11.5
11
11
11.6
21.4
19.8
19.6
18
20.4
18.9
20.7
18
19.6
20.4
19.6
17.6
19.4
19.5
21.5
18.7
19.1
18.9
17.8
19.5
18.9
18.6
19.5
18.7
18
20.5
20.6
19.6
18.8
18.4
19.7
21.2
18.4
18.5
19.3
19.6
20.1
19.7
20.4
19.5
19.4
21.2
20
20.5
18.8
18.2
19.3
15.1
15.4
15.6
15.1
15.4
15.2
15.4
14.3
15.3
15.8
14.3
14.2
14.6
14.8
15.8
14.3
14.6
14.3
14.6
15.8
14.1
15
16.1
15.2
15
14.8
14.3
15.1
14.8
14.4
13.8
15.8
14.4
14.5
16
15.4
15.5
13.4
16
14.3
14.3
16.2
15.2
15.2
15
14.8
16.8
41.3
42.1
45.2
42.1
41.2
41.7
43
41.7
38
41.9
40.7
41.3
40.9
41.7
41.3
41.1
43.4
40.7
42.5
40.3
39.8
39.8
40.5
41.1
42.5
42.5
38.5
43.8
41.5
40.3
40.3
42.1
42.1
38.9
44.4
40.9
42.1
43
38
37.1
41.1
40.9
38.9
40.9
39.2
41.7
39.4
27.3
29.7
29.7
31.1
29.8
29.2
29.4
28.5
29.7
27.8
28
29.7
28.7
26.8
31.1
27.8
27.3
27.8
25.2
28.3
27.8
28.3
29.9
26.8
29.4
29.4
24.4
29.2
29
27.8
30.2
27.1
31.3
29.4
24
24.4
28.7
27.1
27.1
24.2
24
24.4
27.1
28.3
26.8
26.6
26.6
32.2
32.9
33.8
34.9
32.2
33.8
33.8
33.8
34
33.3
35.3
34.7
32.9
32
34.9
32
34.7
34
30.6
30.6
32.9
30.4
34.9
32.4
34.2
34.4
30.4
35.6
33.3
33.5
32.2
32.2
35.1
33.3
30.2
28.7
33.5
33.5
32.2
30.6
29.4
30.6
31.7
34
34
31.5
31.7
20.2
24.9
19.9
22.1
22.4
19.2
24.7
23.5
22.8
19
19.4
22.8
21.6
19.7
26.4
21.1
19.9
21.1
20.9
18.2
22.3
19.7
21.4
20.2
23.5
19.9
18
19.9
21.4
20.6
20.6
20.2
20.6
24.2
20.6
18.7
25.2
25.2
20.6
17.7
21.6
19.7
21.6
23.7
23.7
19.9
24
28.3
30.8
32
31.3
29.8
29.7
31.5
32.9
27.3
28.7
31.7
32
30.6
27.8
30.2
30.6
31.3
29.4
30.4
29.2
29.7
30.2
32.9
31.1
34.7
34
29.9
28.3
32.4
29.9
29.2
30.6
31.1
33.5
32
29
29.4
31.5
28
27.8
30.8
29.9
29.7
28.5
30.8
29.9
31.1
13.8
15.3
15.5
15.2
15.6
13.8
14.2
15.6
13.1
15.1
14.4
15.5
15
14
15
14.8
14
15.6
15.3
12.9
16.6
12.9
14.5
14.4
15.1
14.5
14.3
14.8
15.3
15.3
14.5
13.7
16.7
14.2
14.2
14.3
14.3
15.2
13.9
13.8
13.6
13.8
15
14.3
14.2
14.6
13.8
11.4
11.5
11.8
11
11.2
10.7
11.2
12
10.8
11.3
10.7
11.2
11
10.5
11.6
11.4
11.2
12
11.4
10.6
11.8
11
11.7
11.8
11.8
11
10.1
12.8
11
11.2
11.5
10.8
12
12.8
11.2
11.4
11.5
11.8
10.3
11
11.7
11.5
12.2
12
11.2
11.2
11.8
18
19.2
19.6
19
19.6
18.6
19.4
18.4
17.3
19.2
18.6
18.4
18.7
18.4
18.8
17.6
20.2
21.2
18.9
20.2
20.8
18.6
20.4
20.4
21.8
21.3
18.3
20.7
20.6
20.4
20
18.9
21
20.6
20.2
17.8
18
19.3
19.1
17.8
18.8
19
20.5
19
19.1
19.2
20
13
14.6
16.1
14.4
14.8
14.2
14.2
16.3
15.5
14.9
14.4
15.6
13.8
14.6
15.8
14.2
14.3
16.4
13.8
14.2
15.3
12.7
15
15.2
15.8
14.4
13.2
14.3
15
13.8
16.9
14.3
15.1
15.5
14.5
14.6
13.8
15.1
14
14.6
14.6
15.1
15.2
14.3
14.5
14.8
15.8
40.1
38.9
38.9
41.7
43.2
40.5
39.2
40.9
41.7
43.8
41.9
43
41.5
37.6
36.7
34.8
36.6
35.5
37
35.5
37.4
37.8
38.6
37.6
36
39.5
34
35
35.6
36.2
39
32.6
37.6
36.3
38
37
42.6
37.5
36.1
39.1
39.6
40.5
35
34.5
35.6
39.1
36.6
26.4
25.6
26.4
26.4
26.8
29.2
23.5
25.4
27.3
32.2
28
27.8
28.5
25
26.4
25.9
27.9
28.2
28
26.5
30.2
29
28.8
28.5
25.6
30
25
26.5
25.8
27.4
28.4
25.6
30
27.5
29.6
27.9
31.8
29.2
28.2
27.5
28.6
29.6
26
26.4
27.9
29.7
28.2
32
32.9
31.7
31.1
32.6
33.5
29.9
32
31.5
38
33.1
34.2
33.5
31.3
31
30.2
31.8
31
32
29.2
33.2
32.6
33.2
32.2
31.5
31.7
27
31.6
32
29.5
34.9
30
33.9
31
32.7
30.8
34.8
35.1
32.3
34
31.2
34.9
29.8
30.1
32
33.7
32
21.8
21.1
21.6
20.2
22.1
23.7
19.7
20.6
21.8
25.4
26.4
21.4
19.7
16.2
16.8
16.4
19.3
18.2
15.1
15.4
18.8
18.6
19.7
15.5
15.4
17.3
16.9
18.3
16.2
14.6
19.6
15.3
19.1
15.4
21.3
15.1
19.9
19.6
15.8
17.2
18
17.4
16.1
18.6
15.6
20.1
14.3
30.2
29
27.8
28.3
32.9
31.1
29
30.2
29.7
32
29.9
31.5
29.4
24.9
24.5
24.2
24.9
26.2
25.7
24.5
26.6
25
29.4
24.3
25.5
27.3
22.6
23.7
25.7
23.9
26.7
22.6
28.8
24
28.7
26.8
30.4
27.5
25
25.6
27.2
27.5
22.3
23.5
23.9
29.5
26
15.8
15.6
14.4
14.6
15.4
15.2
15.4
16.1
14.9
16
15.6
14.3
14.5
11.2
12.1
11.3
12.3
11.5
12.5
12.3
13.3
12.1
13.4
11.8
12.8
12.8
10.6
11.5
11.5
11.2
13.4
10.3
13.4
11.1
13.7
13.2
12.5
13.1
12
12.6
12.4
12.6
12.4
11.3
11.9
13.2
11.8
12.4
10.6
11.3
10.2
12
11.3
11.5
11.5
11.8
10.7
11.5
11.1
10.5
9.2
9.9
8.9
9.5
9.1
10
9.4
10.7
9.8
11.5
8.6
9.7
9.2
8.3
8.6
9
9.6
11
8.1
10.5
9.4
10.6
8.9
11
10.2
10.2
10
10.1
10.4
9.5
8.9
9.6
10
9.9
20.7
20.2
19.6
18.4
20.5
20
19
19.3
18.9
21
21.2
21
19.4
17
19.3
17
18.6
17.2
17.2
17.2
19.8
17.8
20.9
17.1
17.6
18.1
15.9
16.8
17.2
16.7
18.9
16.2
19.2
16.4
21.5
18.1
21
20
18.4
18
19.3
18.8
17.2
17.2
18.2
20.3
18
15.8
14.8
14.8
15.3
16.8
16.1
14.8
15.8
13.6
16.8
15.9
14.8
15.3
12.3
12.8
12.2
13
12.4
13.2
12
13.8
12.7
13.2
11.9
13.2
12.4
11.6
12.2
11.8
12.6
13.6
11.6
13.2
12.3
14.4
12.3
14.2
13.1
12.9
12.7
13.8
13.1
12.3
12.3
12.7
13.6
12.7
34.8
36.7
39.7
35.5
36
35.8
37.6
37.6
34.9
33.3
36.2
33.3
36
34
36.2
34.9
37.4
33.8
34
34.4
34.7
35.6
33.8
37.8
38.3
40.3
38.9
39.4
35
40.7
39.6
36.9
35.6
38.2
36.9
36.9
34.8
36.6
36.9
36.9
36.9
36
36.2
35.1
38.8
36.4
38.6
26.3
22.1
31.6
24.3
28
26.4
27.3
28.7
28
24.9
27.1
29.2
25.2
27.3
28.7
27.1
28.3
28.7
27.3
23.5
27.8
26.4
29.7
26.6
30.4
29.2
27.5
29.2
27
29
30.4
28.3
25.7
30
29
26.9
26.4
27.5
27.4
26.4
30.2
28.6
30.2
28.1
27.2
26.2
24.2
29.9
28.3
34.5
29.5
30.8
32.2
32
30.8
30.8
27.8
29.9
32
30.8
29.9
31.3
31.5
31.3
32.2
32.2
26.8
32.6
32.2
32.4
33.1
32.2
32.9
31.1
34.7
33
35.3
34.2
32
29.1
35.5
33.7
31.9
29.8
30
31
32.4
34.6
32
31.2
30
33.4
32.2
34.4
16
16.7
19
15
17.3
17.3
18
19
15.6
17.3
16
14.8
16.5
17
19.2
19
16.3
18.7
19
16.5
16.5
15.1
17.3
16.5
18.7
16.5
15.6
18
19.3
17.7
21.4
17
15.5
19.4
15.6
16.1
14.9
17.7
18.2
16.6
17.5
17.5
16.8
17.1
17.2
17.3
15.3
22.9
27.5
24.9
26
25.9
24.9
25.6
25.2
24.2
23.3
24.2
25.9
24.2
24
27.1
24.9
25.6
25.4
24.2
24.4
24.2
26.6
25.4
27.1
26.4
26.4
26.8
28.3
25
28.5
26.8
25.6
26
26.7
27
25.2
25.2
24.1
25.7
26
26.2
24.1
27.7
25.2
31.6
25.8
29
11.3
12.3
12.7
11.5
12.9
12.7
12.4
13.1
11.2
12.8
11.8
12.6
12.6
12
12.8
12.4
12.9
12
12.9
11.7
12.6
13
13.4
12.4
12.4
13
12.4
13.4
11.5
13.8
14.2
10.9
11.5
12.6
11.5
13.4
12.2
12
12.8
12.6
13.2
12.8
11.5
12
12.9
13.1
13.1
9.2
10.1
10.4
9.4
9.8
10.4
9.4
11.5
9.2
9.8
9.2
10.4
9.2
9.2
10.5
9.8
11
8.9
10.6
9.2
9.8
10
9.6
9.8
9.4
9.4
10
10.5
9.9
10.8
10.6
9.4
9.5
10.8
10.2
10
9.1
9.3
10.4
10.5
10.4
9.8
9.4
9.6
11
10.1
10.4
16.5
16.8
18.2
17.2
17.8
18.9
18.8
18.6
17.9
17.4
17.3
18.4
17.6
16.8
18
18
18.4
17.4
17.9
16.8
17.6
17.6
18.4
18.3
18.1
18.6
18.4
19.8
17.1
19.8
20.7
17.3
17.8
19.5
18.4
18.8
18
17.7
17.8
18.9
19.4
18.7
17.4
19
18.2
17.9
22.1
11.8
12.4
13.1
12.1
13.8
14
13.6
13.6
13.2
12.9
12.6
13
13.2
12.4
14.4
13.8
14.3
13
13.4
12.4
12.6
13.8
13.4
13
12.7
12.9
13.6
13.1
13
14.3
13.1
12.6
12.1
13.6
13.8
14.3
12.4
13.2
14.1
14.4
14.3
13.8
13.1
14.2
13.4
12.6
14.4
36.5
37.5
39.9
34.4
38.7
32.6
34.5
36.7
36.5
34.2
37.8
35.7
33.9
35.2
37.1
37.7
37.8
39.3
37.2
36.1
35.2
35.8
35
37.8
35.7
39.5
38.8
37.9
37.7
38.2
40
35.7
35.7
36
35
37
36.7
32.8
34.8
35
38.7
32.8
36.7
38.8
36.4
34
38.2
26
27.4
20
26.1
23.5
24.6
25.6
28.2
27
28
28.6
25.5
24.3
24.1
24.3
26.2
28.1
24.5
24.4
26.8
25.1
27.7
25.6
29.9
27
29.8
26.3
29
25
25.9
31
28.3
25.9
27.6
25
26.9
23.5
26.2
20.3
23.7
27.1
20.9
23
26.5
24.9
27.8
27.5
30.7
31.2
32.4
30.5
33
29.4
29.2
33
31.6
31
30.7
32.5
29.5
26.9
28.4
30.8
30
32.3
29.4
31
33
28.9
32.5
31.1
29.8
31.5
31.5
32.9
30.4
30.2
35.8
29.6
29.3
29
27.2
32.4
29.5
26.3
31
29
31.4
28.2
30.8
29.8
30.8
29.6
30
15.9
18.9
17.6
18.8
16.4
15.8
18
17.5
16.6
20.4
17.3
16
15.8
17.9
16.2
17.8
17.9
21.4
18.1
16.2
20
16.4
17.9
17.3
16.5
19.2
19
18.6
16.6
16.9
21.3
17.4
14.7
18.6
15.4
16.6
17.2
16.1
17.3
15.4
16.5
17.2
17
17.4
16.5
16.5
20.4
26.8
26.5
31.9
25.2
27.6
25
24.2
25.6
24.4
25.6
25.4
27.2
26
23.6
25.8
25.2
24.9
29.5
27.3
24
26.6
25.6
27
25.8
26.2
25.4
25.9
27
29.3
24.8
33.2
23.3
29.1
25
23.4
25.4
28.3
23.6
26.8
23.6
27.5
22.2
27.6
28.2
26.7
24.4
29.2
12.1
14
13.6
12
12.6
11.3
10.1
12.2
11.9
12.4
11.8
11.9
11.6
12
12.1
12.4
11.1
13.4
12.3
11
11.6
11.5
12.6
10.9
12.1
13
11.6
12.7
12.4
11.7
14.1
10.7
13.2
11.8
10.8
12.9
11.5
10.6
11.6
11.5
12.8
11.3
13.1
12
12.4
9.9
11.8
10.3
11
10.4
9.9
9.9
9.2
9
10.1
9.7
9.7
10.6
10
9.4
9.5
9.8
10.2
9.6
10.9
9.9
8.9
9.1
9.1
9.8
9.4
9.6
10.6
9.9
10.6
10.2
9.4
12.2
8.7
10.9
9.2
8.7
10
9.5
9.2
9.8
9.6
9.2
9.5
11
9.4
10.5
8.9
9.2
17
19.1
18.5
17.5
17.5
16.9
16.3
17.8
18
18.5
18.8
18.6
16.3
17.5
16.8
17.2
18
18.2
17.1
17.8
21
17.1
18.6
15.7
18
19.1
18.8
18.2
18.6
16.9
24.3
16.8
18.1
18
16.8
18.1
16.1
16.4
17.9
16.6
18.8
16
17
17.7
18.4
17
17.8
12.4
13.5
13.4
12.7
12.6
11.9
11.5
13.5
12.5
13
13.3
13.6
11.2
11.5
12.2
11.8
13.2
13
12.2
12.2
12.6
12.3
12.9
11.5
13.6
13.4
13.1
12.1
12.7
11.7
12.9
11.3
13.1
11.4
12.2
13.1
9.9
11.7
12.4
11.6
12.5
11.2
12.9
12.6
12.8
11.5
11.5
35.1
36
35.9
35
35.2
34.9
36
36.4
35.5
34.1
37.1
35.2
37.5
36.3
37.2
37.6
33.6
34.5
36
35.4
35.8
38.3
33.8
36.9
34.9
35.1
37.4
36.9
36
32.9
38.3
37.6
36.7
38.9
37.8
38
38.7
37.1
35.8
38.5
38.5
36
34
38.3
38.7
36.9
35.8
23.4
25.2
25.1
27.1
24.4
26.2
28.1
27.7
27.7
18.7
25
26
26
24.9
26
27.7
24.3
29.2
27.1
27
28.3
28.3
28.7
31.1
28
28.3
30.2
27.5
28
26.6
31.7
30.7
28
25.2
28
31.7
30.4
27.1
30.2
30.4
30.8
30.2
26.4
26.6
33.3
29
26.6
30.6
28.4
28.2
30.1
29.8
28.5
31
29.8
30.7
27.2
29.3
30.4
29.4
31
28.5
30.2
27.9
31.9
31.4
29
30.2
32.4
32.9
33.8
33.1
29.7
34.2
31.1
30.4
32.2
37.4
35.6
31.7
31.5
32
32.9
31.3
32.6
33.5
35.1
35.1
32.9
29.9
33.3
33.8
33.5
31.1
16.2
15.4
18.1
19.5
15.1
14.6
18.8
17
20.6
16.1
17.1
17.3
17.6
16.6
18.8
17.4
18.2
18.3
18.5
17.8
19.2
18.7
17.7
16.8
18
18.2
21.6
16.3
16.3
18.5
19.2
24.7
17.3
17.3
16.8
22.3
18.7
17.3
20.6
18.2
15.8
18.7
19.2
18.2
20.9
20.9
18.5
26.8
26.9
26.1
24.9
26
23.5
27.4
25
24.9
24.6
28.1
25.5
26.5
27.7
25
25.7
24.7
23.6
24.6
25
24.9
28.3
23.5
26.6
26.1
27.3
28.3
26.6
26.4
25.2
28.5
32.2
27.3
24.2
28.3
25.2
26.8
26.6
27.5
27.3
27.3
27.8
27.5
26.4
30.2
30.2
24.7
12.1
11.2
11.6
12.4
13
10.4
11.5
11.2
11.6
11.2
13
11.1
12.3
12.5
12.3
12
11
11
11.9
11.6
12
13.9
12.6
13
12.6
13
13.2
12.8
12.2
12
13.2
14
13.1
12.9
12.7
12.4
12.4
13.2
12.4
13.8
13.1
12.4
11.8
13.1
14
12.7
12.4
9.4
9.9
8.5
9.9
9.2
8.7
9.7
9
8.9
9.5
10.9
9
10.4
10
9.7
9.1
8.4
9.3
9.4
9.2
9.2
10.6
9.4
9.8
9.6
9.3
10
9.8
9.2
8.4
9.3
10.6
10.6
9.8
9.8
10
10
10.3
9.4
10.7
10.6
9.6
9.4
10.8
10.5
9.6
9.6
16.1
16.8
16.8
18.2
17.3
16
17.5
16.9
17.9
16.1
17.5
17.1
18.3
18.1
18.4
17.5
16.6
18.7
15.9
18.2
18.4
18.9
18.2
18.4
18.8
17.7
19.6
18
17.6
19.4
18.6
21.2
18.4
18
18.1
19.6
19.4
19
18.4
19
18.6
18.4
17.3
20
18.9
18.6
17.9
12.2
12.1
11
12.5
12.2
11.1
12.8
12.2
11.5
11.9
13
12
12.7
13
13
12.1
11.1
12.4
11.9
12.1
14.2
14
13.2
13.8
12.2
13.8
14.1
14
12.8
12
13.8
14.5
13.4
12.8
13.2
13.8
13.6
14.4
13
14.4
14.2
14.2
12.4
13.8
14.8
14.2
13.8
36.7
36.7
37.6
35.1
35.3
38.5
37.8
35.1
32.4
39.2
38.3
32.9
38
37.8
34.2
37.6
35.3
34.9
37.4
36.2
38.9
36
33.3
37.4
34.7
38.7
36.2
37.6
34.9
34.7
34
37.8
35.1
39.2
35.1
37.1
35.8
35.3
37.6
35.8
36
35.6
37.1
35.6
35.1
35.8
37.4
29
28
31.3
23.7
23.3
26.6
29.4
25.6
30.2
31.3
30.8
20.9
28.3
32
29.2
31.3
25.4
27.3
32
31.1
29
30.4
25.9
29.4
29.4
28
28.3
27.8
26.1
24.7
26.8
28.5
27.8
29.9
29.9
29.2
29.4
26.8
26.8
29
29.2
28.3
27.8
30.2
29.4
26.8
29.4
32
31.1
33.5
31.1
28.3
34
32.2
29.9
33.8
33.8
35.6
28.5
31.1
33.8
31.1
35.3
31.3
32.2
34.7
34.7
33.1
32.9
29.9
32.6
31.5
34.7
31.3
31.1
29
32
32.2
33.5
30.6
34.9
35.3
32
30.8
31.7
31.1
30.6
33.5
28
31.7
32.9
33.1
30.4
31.7
19.7
19.4
17
18.5
15.3
22.3
15.8
16.8
15.3
17.7
17
19
17.7
16.8
18
20.2
17.3
17.7
19.7
21.1
16.3
18.2
18
19.9
17.7
16.3
16.3
19.9
16.5
17.7
17.3
18
16.3
18.5
18
18
17
18.5
16.5
18
17.5
14.4
20.6
21.8
17.7
23.3
16.5
25.6
27.5
25.4
25.9
24.7
26.6
27.5
24.9
25.6
29.7
26.8
23
26.1
26.6
25.9
27.3
25.4
25.4
25.9
26.8
25.9
24.7
25.6
27.1
24.9
28.5
25.4
25.9
25.6
25.2
28.7
27.1
26.8
26.4
28.5
26.1
26.6
23.3
24
24.2
27.8
23.7
26.4
26.8
27.3
25.6
25.9
12.4
12.9
12.4
12.8
12.4
13.8
11.8
12.6
12.2
13.2
13.6
12.2
12.2
13.4
12.8
11.3
12.4
12.6
13
12.9
12.2
13.4
12
13.4
13.4
13.6
12.2
12.9
12
12.8
11.2
12.9
11.6
14.3
13.8
13.2
12.2
11.5
11.8
12.4
11.6
11.7
12.4
13
12.8
12.4
12.2
10
10
9.4
10
10.2
10.7
9.8
9.6
10.2
9.6
10.4
9.1
10.2
10.4
9.8
9.4
10
9
10
10.4
10.2
10.5
9.2
10.2
9.6
10.4
9.6
9.6
9.2
10.4
9.1
10.4
9.6
10.8
10.5
10.2
10.8
9.2
10.2
10.5
10.5
9.6
10.4
11
10.3
10.3
10.8
18.6
17.9
19.2
17.7
17.1
20
18.2
18.2
17.9
17.8
19
16
17.3
18.8
17.6
18.9
17.5
17.4
18.4
18.6
18.8
19.5
17.6
18.4
18.4
20.4
16.8
17.2
17.3
18.4
17.4
18.6
17.2
19.6
20
19.2
17.6
17.8
18.4
17.9
18.7
16.4
18.2
20.6
18.7
17.5
19.4
13
14
11.5
12.8
13.4
15.5
13.8
12.5
13.4
14.4
13.6
12.7
13
13.4
13.4
13.8
13.6
12.2
13.4
14
13.8
13.6
12.9
14.1
13.4
14.3
12.9
13.8
13.2
13.8
12.9
13.4
12
14.4
14.3
14.4
13.4
12.6
12.8
13.4
14.2
13
13.2
14.3
13.6
13
14.3
38.9
37.4
37.6
35.1
38
36.7
35.6
35.6
35.6
37.8
40.9
34
34.9
35.8
36.5
32.9
36.9
35.8
39.4
36.5
35.8
34.4
36.5
38.5
35.3
36.2
34.9
38.7
37.6
34.7
37.8
39.8
36.5
38
35.3
34.7
38.5
35.6
28.5
29
28.3
26.6
33.3
25.2
29.9
30.8
27.3
29
28.7
25.9
31.3
31.5
27.5
26.8
28.5
29.4
28.3
28.3
27.3
29.7
26.6
25.6
25.4
28.7
28.7
29.7
25.2
29.4
29.7
27.5
29.7
30.4
28.7
24.9
29
29
34
32.9
29.4
29.2
37.8
29.2
33.5
33.8
31.7
32.4
29.2
29.4
31.7
32.6
30.8
28.7
31.5
32
30.2
29.7
28.5
31.7
30.8
31.7
28.5
27.8
32.9
32
29
33.5
31.3
31.5
34
32.9
30.4
24.7
32.9
29
19.2
17.7
16.8
17
20.6
18.5
18.2
26.8
17.5
20.6
18.2
20.2
20.9
17.5
18.5
16.3
15.6
18
21.6
17.7
18.2
17.5
16
17
15.1
16
16.8
15.8
19.2
17.7
18.5
19.4
20.2
17
17.7
17.3
15.3
20.4
27.5
23.5
25.4
24.4
28.3
24.2
24.9
27.1
27.3
28.5
27.3
24.2
31.5
25.2
24.5
24.4
27.8
25.9
29.7
26.4
23.5
24.7
24.9
25.6
24.9
23.7
26.8
26.4
27.1
25.4
26.6
29
28.5
27.1
25.6
24.2
25.6
26.8
13.3
12.7
13.2
11.8
15
12
13.2
12.4
12.4
12.7
12.9
11.4
13
12.9
11.6
11
11.6
11.8
12.8
12
11.2
12.6
12.6
11.8
10.6
12.4
13.4
12.8
14
12.4
13.4
13.1
13.3
12.9
12.4
12
12
13.4
10.3
10
10
9.4
11.5
9
11
10.2
9.8
9.1
9.6
9.6
9.6
9.8
9.6
8.6
9.8
9.8
10.5
10
10.2
10.2
10.7
10.2
10.4
10.2
10.8
10.5
11
10.8
11.2
10.4
9.8
10.4
9.8
10.2
9.8
10.8
19.1
18.2
17.8
17
22.6
17
19.2
18.2
17.6
18.2
16.8
16.6
17.8
17.9
17
16.4
17.2
18
19.5
17.1
17.5
17.7
17
16.8
17
17.9
17.9
18.4
18.9
20.2
18.4
17.6
18.9
19.5
17.3
18
18.6
18.7
14.2
13.8
14.2
12.2
13.8
11.8
13.8
14
12.7
13.2
13.4
12.6
13.7
13.4
11.7
12.6
12.9
12.7
14.4
12.8
12.9
12.4
13
12.9
12.6
13.2
12.9
13.8
13.2
12.8
14.2
13.8
12.4
14.4
13.6
13.6
13.3
13.8
sho.gi
che.gi
wai.gi
nav.gi
hip.gi
thi.gi
bic.gi
for.gi
kne.gi
106.2
89.5
71.5
74.5
93.5
51.5
32.5
26
34.5
110.5
97
79
86.5
94.8
51.5
34.4
28
36.5
115.1
97.5
83.2
82.9
95
57.3
33.4
28.8
37
104.5
97
77.8
78.8
94
53
31
26.2
37
107.5
97.5
80
82.5
98.5
55.4
32
28.4
37.7
119.8
99.9
82.5
80.1
95.3
57.5
33
28
36.6
123.5
106.9
82
84
101
60.9
42.4
32.3
40.1
120.4
102.5
76.8
80.5
98
56
34.1
28
39.2
111
91
68.5
69
89.5
50
33
26
35.5
119.5
93.5
77.5
81.5
99.8
59.8
36.5
29.2
38.3
117.1
97.7
81.9
81
98.4
60.5
34.6
27.9
38.9
123.5
99.5
82.6
82.5
95
58.5
38.5
30.4
39
116.5
103
85
94.5
103
59
33.5
29
40.5
113
99.6
85.6
89.2
98
59.1
35.6
29
35.8
107.5
101.5
78
89.5
95
57
36
29
34.5
112
104.1
82
84
97
56
34.5
29.5
39
112.2
100
88.3
93.5
105
65.8
37
28.8
40.9
120
93.8
73.6
74.9
90.1
54.1
31.2
26.9
36.4
109
98.5
78.5
86
94.5
55
34.5
28.5
38
118.5
104
87.3
88
101.1
59.5
37
30.5
39.8
116
100
92
91
98
57.5
32
27.6
37.5
111
100
80
83.7
99.5
57
37
30
37.5
117.7
99
74.5
75.9
92.2
53.4
31.2
26.9
36.2
123.9
101
90.6
89.6
101.2
59.5
37
28.3
35.4
120.6
101.6
81.4
81.6
98.8
61.3
39.4
31.9
38.5
129.5
108.8
89.5
89.5
106
59.5
37.5
30.1
39.9
115
100
85
94.5
105
62
35.5
28.5
38
116
88
73.5
77.7
97
56.3
32.5
27.8
39
107.8
88.7
75.8
83
89
52.6
31.2
26.5
37
100.2
84.5
74
81
93.5
50.5
27.5
24.8
34
113
93.6
77.5
82.1
95
56.5
32.8
26.2
37.6
117.9
105
74
72
90
54.2
34.1
28.6
36.2
112.5
90.9
74
78.8
96.4
51.8
29.8
27
36.4
110.5
91.2
82
89.5
100
57.5
32.8
28
40.7
112
98.4
73
83
95.4
56.3
36.4
27.5
37.2
104
85
70.5
84
90
50
29
26
36
114.8
97.2
75
77.2
91.3
49.5
31
26.1
36.3
108
91.5
72.1
79.2
91
54.9
29.5
24.5
36.1
111.2
91.2
78.8
78
93.2
55.8
31.9
27.4
36.4
118.3
101.1
77.5
78
97
55
37.7
29.9
38.3
115.2
104.3
91.5
93.2
103.9
62
36.3
29
36.7
129.9
110.8
84.9
83
102.6
66.4
42.3
30.9
37
112.9
96.3
79.1
78.3
97.1
60.1
35.5
28.8
36.9
112.2
102.7
77.9
77.9
90.7
56.7
35.4
28.3
35.6
117.1
103.9
91.7
89.4
101.8
61
35.7
29.4
37.7
118.7
105.6
86.6
87.3
103.9
63.2
37.8
29.7
39
109.2
128.1
113.3
108.4
118.7
126.3
124.2
126.7
103.3
101.2
104.3
113.2
121.9
113.1
108.5
113.9
112.6
110.2
108.7
104
115.2
111.9
127
111.2
122
114.5
109.5
110.8
118.8
108
114.3
105.4
115
119.5
130
113.3
113.2
106.9
113.8
117.3
124.2
123
117.8
118.8
112
113
116
95.8
111.2
100
91.6
108
109.6
105.7
109.1
88.8
86.1
91.3
100.6
105.5
97.5
94.4
99.6
98.1
93.6
93.4
92
99.2
97.6
108.8
91.9
105.2
98.3
92.5
92.5
101.6
94.6
92.5
88.2
91
106
115
100
94.7
92.5
96.7
97.4
106.7
106.2
103.6
98.3
87.8
99.8
104.6
84.7
90.3
79.7
73.1
79.8
81.6
76.8
85.9
73.3
69.9
72.7
82.7
90.1
82.9
77.9
92.5
77.8
72.7
75
76
82.7
80
107.1
76.2
90.2
89.4
80.9
73.5
70.9
76.1
81
72
76.8
86
98.5
79
77.5
75.2
82
79.6
75.2
88.6
81.5
79.9
73.5
80.3
81.5
84
93.5
87.1
75.4
82.5
86.5
83.4
90.4
77.9
67.4
83.2
83.5
89.2
83.6
79
96.2
77.2
77.3
79.2
83
84.2
85.7
107.2
78.1
88.6
87.4
78.5
76.4
76.7
78
85.2
72
80
92
106.6
82.5
80.5
80.2
82.2
80.8
77.8
88.3
83.3
82.4
77.5
80.8
85
101.4
108.7
98.4
86.5
94.8
100.9
98
100.9
85.7
84.1
91.4
98
104.5
95.8
91.7
103.4
90
91.7
94
93
93
97.4
108.3
90
100.2
97.7
96
92
95.3
86.3
92.5
85.5
94.5
103
116.5
98.5
92
91.6
92.7
95
94.5
100.5
91.8
87.5
94.9
93
92
60
66.9
61.1
50.6
58.3
61.7
56.8
61.3
46.9
50.8
51.2
55.8
62.7
52.6
57.1
58.5
52.4
51.9
53.8
54.5
56.6
57.8
67
52
60.8
54.8
59
53.1
56
52.4
54.7
50.2
54.6
60.6
67.8
62.1
54.2
49.6
54.6
54.2
57.4
63.4
55
54.4
53.5
55.4
54.1
35
40.2
36.3
30.8
39.8
39.5
37.9
40.1
30.5
31.5
27.8
33.1
36.3
34.5
31.2
34.5
33.2
32.1
34.2
29.5
32.4
33.8
39.6
30.7
35.7
31
31.5
30.6
36
28.6
32.3
28.6
33.2
34
35.8
34
30.9
29.2
32
32.6
36.7
36.9
33
33.5
34.3
33.3
33
28.5
32.4
28.6
26.1
29.6
31.7
30.9
30
24.8
26.6
26
28
29.6
27
27.5
28.4
26.4
27.4
27.9
26
27.6
28.6
30.6
25.8
29.4
26
26.3
27.1
28.6
23.9
26.8
24.8
28
29.8
27.2
28.8
26.6
26.1
27.1
27.4
29.9
29.4
27.8
27.3
28.5
28
28
38.4
39.2
34.5
31.7
34.2
38.8
35.9
36.8
31.1
32.8
34.8
37.9
38.4
35.2
36.6
38.4
34.2
33.5
36.1
37
35.8
36.2
40
34.8
39.2
36.4
36.1
36
36
34.5
35.8
34.9
37.5
38.8
38
39.6
36.5
36.2
35.6
36.5
38.1
38.4
35.4
36.8
36.5
36
35.1
112.8
125
108.3
108.2
113
115
123
120.2
114
102.9
112.5
104.5
111.3
117.2
112.8
104.8
117.7
107.7
125.2
109.1
122.6
117.3
109.1
116.7
124.9
118.6
108.8
121.9
117.3
115
134.8
113.8
119.4
117.9
127.3
118.8
122.4
111.5
113.2
115.3
122.5
114.4
112.8
112.2
119.4
108.4
122.4
86.5
110
93.2
90
98.4
107.2
108.3
105.7
88.5
79.3
90.9
90.2
91.6
105.2
97
85.3
99.6
94.3
111.8
94.3
106.1
102
94.8
102.9
115.8
105.4
87.1
104.1
95.8
98.6
118.7
100.9
98.5
96.9
110.7
108
109
104.2
100.5
105.7
112.4
96.2
97.5
90.9
108.4
94.3
109.1
74
104
76.2
76.5
81
88.8
94
83.4
77
75.4
80.3
68
80.6
88.6
81.1
70.8
73.3
75.9
86.2
75
101
90
75
75.9
96
84
67.1
82.5
83.7
76.7
105.2
90.6
85.7
82.5
94.7
105.2
86
90.9
92.4
96.5
98.4
76.7
94.8
80.1
97.4
73.7
76.1
76.5
99
83.8
77.7
80.5
86.8
98
86.5
79
78
80.8
67
78
94.7
88.2
84.9
82.1
79.1
93.5
82.2
99.7
92.3
79.6
77
95.9
90.4
80.4
90.1
84.2
85.8
105
93.3
92.9
90.8
92
103.4
90.2
92.7
92.4
98.2
101.5
83.5
98.2
79.8
103.7
74.5
90.1
91.3
111.7
92.8
91.2
96.2
100
108.2
101.1
93
88.6
92.8
81.5
91.3
94.7
93.9
89.4
89.3
92.6
96.3
88
105.5
102.3
91.6
93.4
103.6
94.8
85.9
98.4
98.4
93.3
115.5
97.7
98.6
94.9
101.3
108.1
98
100.2
97
97.4
107.9
93.9
98.6
91.3
105.3
88.2
93.3
53.5
63.2
55.2
54.2
56
61
66.8
61.3
51.7
50
53.9
49.5
55
58.3
53.5
55.8
55.4
54.4
59.1
53.8
60.2
60
49.4
55
62.2
57.6
46.8
57.7
56.2
56
69.9
58
55.5
54.4
60.1
60.5
59.5
51.8
50.9
54.3
67.4
50.4
48.3
56.2
55.6
52.3
51.7
30.5
37.5
31.2
33.1
32
34.6
35.6
34.7
33.5
25.6
32.5
27
30.7
36.9
33.7
28.7
36.3
33.2
36.3
36.3
38.6
34.6
30
35.2
38.2
38.7
30.3
37.9
33.7
35.7
39.4
34.8
35.3
32.8
37.2
38
40
30.1
32.9
31.9
39.2
32.1
31.1
32.9
36.6
29.6
37
26.1
29
26.2
27.2
27.4
27.9
27.3
29.4
27.9
22.7
28
23.6
25.3
28.8
28.6
25.5
32.5
27.9
28
28.9
30.3
29.7
26.5
28.7
30.1
30.2
25.4
31.6
28
27.6
32.1
28
28.7
28.7
30.9
30.2
31.2
26.8
29
28.5
30.5
27.7
27
27.2
28.4
26.2
30.6
36.6
41.2
36.8
35.5
37
38
39.5
39.4
38.4
33.8
36.5
34
35.5
40.3
35
38.5
34.3
34.8
38.3
34.5
39.5
38.2
31.7
37
41.2
38.6
32.7
37.8
38
34.7
42.2
34.1
39.3
39.2
40.5
36.9
38.3
38.1
37.7
37.7
42.6
36.1
37.7
36.2
38.2
35.2
36.8
128.8
118
116.5
120.4
123.1
117.2
113
109.4
105.7
119.7
118
104.3
114.1
119
113.8
118
116
108.3
129.2
109.2
124.3
122.6
122.4
114.9
111.1
126
115.5
124.7
125.3
118.2
124.3
118.3
122.3
116.5
123
117.6
117.5
117.3
114.5
122.9
115.5
116.1
121.6
131.6
124.5
115.6
117
115
104.4
100.1
108.4
107.3
101.8
94.5
91.7
95.9
110.5
104
86.8
106.7
102.5
103
95
99
89.7
111.5
94.1
118.3
106.5
110.4
102.3
98.5
111.6
106.7
110.4
114
101.8
109.6
100.7
104.3
104.2
107.4
101
103
107.2
99
100.3
100.2
99.8
107.5
110.1
107
105.6
103.6
95.6
101
84.5
98
101.6
87.8
80
81.8
84.4
85
90
72.9
81
86.5
93.9
77
75
80.6
100.5
81.2
103.4
90.3
98
86.5
77.9
89.1
93.9
85.3
98.5
79.5
94.9
76.5
88.4
84.2
87.6
83.7
92.1
89.9
88.7
83.9
79.5
84.5
89.2
90.7
88.8
103.6
98.5
101.9
98.9
84.5
101.8
103.8
90.2
85
82.9
86.8
83.5
86
73.4
80.2
89
98.6
78
75
80.8
107.3
84
106.2
101.1
98
87.7
87.3
95.1
111.8
82.9
103.8
90.1
94.7
87.2
89.6
84
89.4
91.1
91.3
94.7
91
89.4
88.7
92.6
88.4
91.9
97.5
100.7
99.9
107.9
103.3
94.4
101.5
110
98.4
95
98.3
99
95.7
96
89.5
93.7
97
103.6
93
90
90
109.5
91.6
108.5
101.6
99.6
91.9
90.8
104.8
111.4
96.5
108.1
95.3
104.3
96.3
98.8
93.2
106.7
99.9
103.8
107.1
100
103.9
95.3
99.5
107
101.7
103.8
100.6
103.6
64.6
54.4
54.7
56.9
57.8
55.6
52
56.3
55
59
52.5
51
54.8
57
60.5
52
50.6
55.5
61.8
51.5
60.5
57.2
56.7
55
50.8
62.7
62.8
57
61.3
54.8
59
54.2
54.8
55
60.9
56.8
56.6
59.2
57.5
59.8
52.5
59.2
56.9
58
61
55.3
57.5
37.1
38.1
33.9
38.2
34.9
33.1
31.5
31
30.5
39.2
33.5
29.8
35.5
34
34.4
32.6
32
28.9
37.4
33
35.4
35.4
36.4
35
35
37.9
36.2
39
37.2
34.2
35.9
33.8
35.5
33
38.3
33.5
33.3
35.3
34
36.1
34.6
34.3
35.6
36.8
36.7
33.6
33.7
30
29.8
28.6
29.9
28.9
28.4
26.5
25.7
26.4
29.9
29.1
24.8
30.6
28.4
28.5
28.4
27.3
25
31.6
27
29.7
28.6
29.2
28.9
28.4
31.2
29.7
29.8
31.4
28.5
27.8
27.7
29.7
25.4
31.2
27.7
27.7
26.9
28.3
29.4
25.8
29
28.5
29
28.6
26.9
29
41.8
39.7
38.5
37.7
40.3
38.2
36.9
35
36.1
37.9
36
32.6
36.9
38
40.9
34.4
33.8
34.6
41
35.2
42.3
40.4
40.9
38.3
35.5
41.1
42.8
36.8
41.9
36.6
37.7
36.4
37.7
35.6
39
38.7
37.1
36.6
40.9
37
35.6
36.5
37
36.9
38.4
37.8
38.7
108.6
120.2
116.2
115.4
120
110.3
119.7
123.5
107.8
118.7
120.7
118.7
118
105
110.6
123.1
121
111.7
111
112
115.9
121
123.6
120
128.7
124.5
112.4
112.2
127
115.3
111.5
118.3
118
127
124.4
112.4
125.8
131.7
117.3
107.6
122.4
117
119
123.5
121.4
112.3
113.2
97.1
109.8
103.3
103.7
108.5
97.8
112.7
111.4
95.1
100.2
106.3
109.5
106.3
91.5
104.9
109.6
102.5
101.2
98.7
96
104.2
103
107
101
112.1
103.4
100.3
95.7
108
101
98.6
101.6
99
116.7
105
95.1
106.7
116.6
103.5
90.4
107.5
100.8
104.2
104.9
112.8
95.7
104.9
82.9
90.5
84.5
86
84.2
85.7
112.1
99.7
84.7
80.3
98.6
90
86.6
80.2
109.2
88.4
81
88.8
78.1
81.5
87.6
92.5
97
82
99.5
93.8
79.1
85.8
90.8
85.4
91.6
79.7
86.1
113.2
79.5
85.4
97.9
94.7
86.1
84.9
92.2
83.7
97.8
98.6
89.5
82.9
90.1
88.1
92.3
94.5
93.8
88.9
89.5
105.9
102.9
92.9
92.4
111.7
96.2
93.9
85.7
104.4
92
84.5
90.8
78.6
80.5
89.6
88.5
95.5
82
97.8
92.7
80.4
94.7
92.4
86.9
102.1
82
90.8
102.9
85.8
84.1
94.7
93.1
90.5
83.7
88.6
82.5
93.6
99.2
96.9
89.6
90.8
91.2
95.2
98.2
97.1
97.5
94.9
106.3
105.8
96.7
96.4
118.7
104.3
95.9
89.2
101.7
95.1
105
101.3
92
89.5
100.5
94
104.5
98
107.4
112.2
94.3
106.8
100.3
101.8
106.7
98.4
101.3
107.9
92.7
94.3
104.6
103.3
96.7
97.9
97.5
97.7
102.5
103.3
100.9
94.8
96.6
51.7
52.4
53.7
53.1
58.8
51.7
56.9
57.8
54.6
53.8
70
63.5
53.6
48.5
56.4
52.5
56
62.5
56.5
52
60.7
55
56.6
59
60.5
66.2
51
60.6
56.5
57
57.8
58.1
56
57.7
51.8
52.7
60.8
58
55.2
51.8
53.7
53.3
58
55.3
54.9
51.9
55
30.7
35.8
32.5
33.9
36.6
32.2
35.7
36.5
32.8
35.7
37.1
39.4
34.4
28.7
34
39.4
31.5
35.2
35.7
30.3
36.5
36
34.4
35.4
35.5
34.8
32.6
33.6
36.8
34
32.3
36.5
33.5
37.4
36.2
31.2
36.2
42.3
34.5
28
34.3
32.5
35.8
35
38.5
32.2
32.9
25.7
28.7
27.8
27.3
29.9
26.4
27.8
30.5
25.3
29.2
27.8
29.9
28.6
25
29.2
29.8
26.5
28.9
29.2
25
31.1
28
28.9
29
28.8
30.1
27.2
27.3
29.3
27.1
27.9
31
28.3
28.9
27
25.9
28.7
31.9
27.7
25.2
27.6
27.1
29.4
29.3
28.7
25.3
26.5
33.9
32.5
36
35.7
34.2
34.4
37.3
39
36.6
38.4
37.5
37.4
35
35.4
39.3
34.5
38.5
40.6
36.4
36
40.7
36.5
40
38
42.9
45.7
36.1
37.5
37.5
39.4
41.8
38
37.7
37.8
33.9
37.4
37.7
39.9
37.3
37.5
36
35.4
39
35.9
35.9
33.4
35.6
121.7
116.6
117.8
118
131.1
121.4
116.3
121.8
118.2
126.3
121
123.1
114.9
95
99.5
88
97
103.3
93.5
93.3
94.5
98.6
115.5
97.9
97.7
100.5
88.7
96.6
92
90
104
90.1
104
91
111.4
96.2
117.1
101.5
95.1
97.1
101.4
103.7
89.2
86
98.1
114
95
109.1
105.4
104.3
100.5
111.8
109.5
101.2
103.3
101.6
103.1
104.6
104.3
95.9
83
78.5
75
86.5
91
79.5
77
88
85
98.8
79
77.6
85
76.7
76.7
82
79
89.5
73.5
90
80
94.5
83.8
95.2
91
80
81.7
89.6
90.9
78.5
78
80.2
99
80
78.9
80.7
94.3
70.2
83.6
91.9
71.8
85
85.7
96.5
82.4
86.3
83.2
66.5
61.5
61.2
78
70.5
66.5
58
74.5
73.5
90.5
66.5
61
69.5
62
63.4
71
59
74
60.5
75
65
82.2
70.2
85
75
63
70
72.6
78.7
61
64.2
63.1
85
66
91
87.4
99.4
79.3
92.7
96.5
82.3
90.8
91
99
85.7
87.8
88
79
70.5
66.5
91
80.5
78.5
64
87
92
103.5
74
71.8
81.5
74.1
69
69
79
92
68.3
80.5
78.3
94.2
82.5
91.2
85
76.5
81.5
86.3
83.5
73
69.8
78.9
92.5
78
98.1
95.5
100.4
92
101.5
103.3
87.6
97.9
95.9
111.8
99.9
103.3
100.6
92
90.5
91
99.5
91.5
94
85.5
104
104.1
108.1
90.3
91.6
94.4
80.9
87.7
88.5
88.5
101
88.5
99
91
110.2
94.2
111
103
90
96
93.7
101.5
82.5
89
93.9
106.4
92
55.7
56.8
59.1
51.7
59.5
57.7
50.1
55.2
50.9
62.3
63.3
59.7
57.8
53.5
57.7
53
61.5
55
54
49.5
64
65.3
61.1
52
53
55.8
48.8
54
54.5
51.2
61.5
54
59
53.5
69
54.1
68
62
51.1
57.9
56.4
59.9
49.5
53
57.1
65.6
52.5
38.5
38.3
35
32.1
40.4
36.5
34.2
35.2
34
34.8
38.6
36.4
34
24.3
27.8
24
28
26.9
26.5
24.1
29.2
29
33.6
24.8
25.4
25.9
24
25.6
26
23.5
31
24.6
28.7
27
32.5
25.9
34.4
31.5
24.6
26.3
27.4
29.5
24.5
23.2
26.4
31.6
25
30.1
28.6
26.7
26.7
31.7
29.1
29.2
29.4
28.4
27.5
32
30.4
28.2
20.5
24
22
24
22.7
22.5
22
26.2
23.4
26.6
21
22.6
22.9
20.5
21.6
21.8
21
26.5
20.6
24.9
23
26.8
23.2
28.3
26.5
22.3
22.6
23.4
25.3
22.5
21.2
23.1
26.6
22.2
37.2
35
35.5
33.2
36.7
34.6
34.1
34.9
35
41.7
38.4
39.3
36.3
32
38.5
32.5
35.2
33
34
32.5
38.5
35.3
37.2
32.2
34
36.1
30.8
34.4
33.5
32.5
38.6
29
37
32
40.5
34.3
40.1
38.2
35.2
37.2
37
35.4
32.5
33
35
39.6
33
87
100.8
112.2
98.7
100.1
100.3
100.5
101.2
96
92.8
95.5
98.7
96.9
91
106.3
99.8
105
106.2
97.7
97.4
96.3
98
94.5
101.4
95.1
101.1
97.4
104.8
94.5
103.2
110.8
94.6
96.6
102.8
96.9
95.6
92.4
93.7
96.1
100.1
98.8
92.2
97.3
90.5
110.5
103
109
75.5
82.6
94.5
83.9
92.8
85.3
84.4
87.6
81
84.1
88.2
88.1
84.9
81.2
91.6
88.4
87.6
91.3
87.2
82.2
82.1
82.6
86.5
85.3
84.7
86.8
85.2
93.9
84.5
90.7
97.4
83.3
82.1
92.2
83.6
82.6
77
79.3
84.3
85.6
85
79.1
85
79
96.2
86
89.8
65
63.2
83.6
68
75.7
65.5
66.9
67.9
67.8
63.2
73.1
65.3
65.6
62.7
81.8
72.1
68.6
80
64.9
61.7
64
58.6
68.3
69.5
70.5
69.8
69
81
71
73.6
96.3
65
62.8
83
67.6
65.4
61.6
63.2
59.4
62.7
66.6
64.6
65.7
63
78.5
68.2
68.5
76.7
70.5
94.2
76.1
88.6
74.4
79.7
82.7
73
75
80
75.8
75.5
75.4
96.5
87.3
80.7
97.9
75.9
66
73.6
73
89.2
74.9
86.1
76.5
76.3
93.2
80.5
79.8
104.2
68.2
70.6
101.4
86.2
74.8
74
75.5
74
74
82
82.5
77.7
79.2
93.4
76.2
80.2
86
89.1
104.1
88
102.6
95.9
98.8
93.5
92.9
86.9
94.9
95.3
93.3
90
99.3
95.6
95.8
104.6
92.2
80.7
98.1
89.6
94
94.7
94.1
93.7
86.7
105.9
97.5
105.3
102.6
91.6
83.9
108.1
99.1
89.3
89.9
85.8
85.8
96
98.7
94.9
90.5
86.6
103
97.9
98.1
51
55.8
61.5
52.2
64.3
53.7
59.2
57
55.8
52.1
57.2
55.7
57.4
54
60.7
59.2
56.6
62.7
53.1
50.3
56.8
54.9
57
55.7
54.6
55.7
51.5
65.5
59.5
65.8
57.5
55.3
51.5
65
57.5
53.7
53.6
51.6
51
61.5
60.3
54
56.1
48.5
59.6
59.8
62
24.5
27
31
26.2
31
27.8
28.5
29.6
26.3
26.5
27
27.7
27.7
25.3
28.3
29
28.5
30
28
23.7
25.8
27.1
26
24.9
28
25.4
26.6
31.3
28
29.5
34.3
27.7
24.6
29.8
26.4
26.4
26.3
24.2
26.9
28
30.4
24.7
29.4
26.4
30.2
29.8
30.1
20.5
23.6
25.4
23.2
24.9
23.9
23.7
24.5
23
23.5
24.3
24.5
24.2
22.7
25.2
24.8
24.1
23.1
24.2
21.6
23.9
23.1
22.6
22.8
23
23.4
22.7
26.8
23
26.6
26.5
23.2
21.4
24.6
23.3
23.8
23.1
22.4
23
23.6
25.2
21.7
23.1
22.5
25.9
25
26.2
31.5
33.6
37.2
33.2
35.5
35.6
35.9
37.1
32.3
32.3
34.9
33.1
35.1
32.6
35
34.3
35.6
36.3
34
30.5
33.7
33.2
35.9
34.9
33.5
35.9
31.6
38.1
34
38.8
38.3
33
34
38.1
38.5
34
33.3
32.5
32.8
35.4
35.7
37.4
33.2
32.2
37
36.8
40.9
104.8
109.2
117
93.9
105.5
99.4
89.5
98.5
94.9
96.3
96.8
102.5
95.2
103
99.1
104.1
99.5
110.2
107.1
95.7
103.4
94.6
104.5
97.7
96.4
103
103.4
109.5
110.7
102.2
129.5
99.2
104.7
98.9
98.5
102.2
100.2
85.9
99.8
93.3
107.3
90
101.5
105.1
101
91.9
112.1
84.5
88.2
99.5
76.1
85.8
82
77.5
85.7
78.8
88
80.2
85.6
81.3
84.6
82.2
84.9
81.5
89.9
89.8
80.8
88.4
80.2
89.5
83.7
82.5
85.5
88.3
91.5
92.2
80.5
108
80
89.5
84.9
80.8
81
88.7
74.5
81.9
75.8
88
72.6
88
86
85.5
80.4
98.1
68.8
69
78
62
65.8
65
64.9
71.5
61.4
75.4
67.2
69.5
57.9
64.4
62.3
68.7
68
66
71.2
64.8
78
60.7
75
68.6
67.1
68
71
76
70.3
69.5
101.5
67.2
68.7
66
67.5
65.2
64.2
61
60.2
62.6
72.7
58.5
67.5
66.1
68
64
90.1
70.6
77.6
87.5
70.8
70.5
77.2
74.5
82
78.8
90
78.3
75.5
66.4
77.9
68.7
78.6
84.6
79.9
85.7
79.8
85.6
77
95
83
75
84.5
87.1
82.5
82.8
81
105.5
75.2
81
81
75.4
75.9
76.8
65.3
64.2
72.9
76.7
67.2
79.5
73.2
86.1
85
90.1
94.8
96.5
103
86.8
89.3
89.5
88.4
100.5
94
101.3
95.5
95.3
84.1
91
83.9
93.1
92.3
97.1
97.5
92
112.1
89.9
104.9
94.2
90.4
99.5
98.7
103.5
100
95.2
114
91.2
93.8
92
85.8
95.4
88.4
84.5
91.7
87.4
95.9
84.3
96.5
91.8
101
92.6
95.2
56.5
57.6
64.8
52.6
57.4
53.4
53.4
60.4
56.4
63.1
54.7
57.6
49
53.4
52.8
55.2
55.4
59
58.2
57.4
75.7
53.3
63.2
58
53.2
60.8
59.2
64.8
59.6
56.2
70
53.6
58
56.2
53.8
58.5
56
51.5
53.3
54
56.6
52.2
56.3
54.4
59.6
54.8
53.8
27
28.6
31.1
24.3
27
26
25.6
28
27.1
28.4
27
28.5
26.6
26.6
24.4
28.2
27.4
27
28.2
26.5
33.8
25.2
29.6
26.2
27.3
26.5
28.2
29.5
30.8
27.4
40.3
27.1
30
26.4
24.8
27.2
29
22.4
26
26.4
29.5
25
28.4
27.4
28
25.6
32.1
23.4
25.2
26.6
22.3
23.2
21.4
22.4
24.2
22.8
22.6
22.2
24.4
22.2
23.3
22.1
23.8
23
24.2
25.2
22.6
24.6
22.4
23.9
22.1
23.6
24.2
23.6
25.2
25.4
23.8
30.8
23.2
24.4
22.6
21.5
25.3
23.8
19.6
23.2
21.8
25.3
20.7
24.6
23.8
23.3
20.7
25.8
34.4
37
35.2
34.2
36.8
34
30.9
36.6
35.4
37.6
36
35.2
33.6
32.7
32.4
34.6
34.5
37.2
34.2
31
38.2
34.2
37.6
32.2
35.9
40.5
35.6
39.2
37
35.4
45.6
34.6
35.9
35.4
33
37.5
33.9
30.4
36
34.5
36.8
31.7
35.6
35
36.1
32.7
34.7
98.2
102.5
98.4
96.8
103.9
92.7
105
94
101.5
92
108.5
93.8
99.8
100.3
101.5
94.7
103.1
94.5
97.1
98
102.4
109.1
94.7
98.2
101.5
96.6
106.1
100.1
105.3
99.8
103.9
111
99
102.5
105.6
99.5
106.5
104.1
99.7
106.6
97.2
100.8
100.7
99.1
108.9
109.8
99.5
82
89
85.8
85.9
82.5
74.5
89.4
80.3
85.6
83
88.2
85.5
80.6
81
83.6
79.4
82.9
83.2
78.1
82.4
90
92.4
86.7
84
86
84.5
91.2
81.1
87.6
88.2
88.2
104.2
84.8
84.3
91
90.5
89.6
89.3
90
88.2
83.5
91
88.2
82.2
98.9
97.9
81.7
64.1
72.4
71
69.1
66.1
59.5
71.5
65
71.5
63
70
70.4
64.3
66
70.5
62
67.6
65
64
70.5
79.2
71.1
74.7
62.9
70.6
61.6
74.2
65.5
67.7
72.9
72.1
93.4
60.7
69.2
75.5
85.6
71.6
75.5
73.7
67.9
71.2
69.3
75.6
63.8
83.6
84.9
66
74.1
80.3
85
77.2
74.9
65.5
80.6
73.3
82
72
81.2
82.4
75
73.2
78.5
73
73.9
80.9
75.9
81.6
95.2
91.5
90.8
76.8
91.9
81
98.2
82.3
84.2
97.4
96.3
111.1
78
85.3
90.7
111.7
92.7
98.9
92.7
86.9
83
85.9
94.7
81.8
108.6
98
85
96
89.9
92.7
94.1
93.8
78.8
96
84.9
97.5
86
96.8
93.5
93
90.2
91.9
88.5
90.2
97.6
95
98
97.4
98.2
100
95.5
101.9
87.6
102.6
90.4
92
102.2
106.7
109.8
89.1
93
98.6
112.1
95
100.2
101.2
100.8
96.5
93.2
95.8
97.6
108.3
102.4
94.3
53.7
52.6
57.3
56.2
54.2
46.3
56.9
50.8
63
53
59.8
57.5
55.6
54.8
56.8
53.6
56.4
62.2
55.9
61.4
61.7
55.3
59.4
52.8
62
51.6
61.5
53.3
54.3
60.1
62
67.7
52.6
53.9
62.7
64.3
56.8
57.8
57.4
60.2
52.4
55.4
58.5
59
63
59.9
56.4
26.6
27.6
28.4
28.9
27.8
23.2
26.8
25
28.4
24.1
30.1
28.3
28.2
26.8
30.5
24.7
30.2
27.2
25.2
27.2
27.8
29.6
31
26.4
29.1
27.4
31.4
26.8
28.2
29.9
27.3
35.7
26.6
27.9
31.5
31.3
27.2
30.3
28.1
31
25.2
29.7
30
27.8
31.9
32
28
23.2
23.8
23.6
23.1
24
20.8
22
22.2
23.5
22
25.2
21.9
23.8
23.8
24.3
22.4
24.2
22.8
23
23.2
23.4
24.6
23.7
23.1
24.2
23.7
25
22.3
23.8
24.1
23.1
28.6
22.8
23.7
24.8
25
24.3
23.8
23.3
26.6
21.7
24.1
22.2
23.6
26
25.7
21.1
35.2
33.2
34.2
35
35.3
31.6
33.8
31.6
39.1
30
35.8
33.1
35.6
34.7
35.8
33.5
34.1
38.6
32.3
35.6
36
34.3
35.7
34.6
37.2
32.4
37.6
34.2
33
33.8
34.6
41.5
32.5
35.5
37.2
35.5
36.2
37.3
33.9
36.6
33.7
34.8
34.6
35.9
38.1
37.6
32.1
100.5
97.4
105
102.9
93.9
114.2
95.9
98.7
91.2
105.1
102.3
93.1
101.7
105
96.4
103.5
99.8
87
105.2
102.1
101.3
99.6
99.4
99.4
99
108.2
96.4
101.4
98.2
100.6
108.4
100.8
94.8
108.2
110.7
102.6
98.1
92
98.6
96.1
107.7
95.4
99.3
115.2
96.7
109
95.1
86.1
87.1
76.8
87.9
81.6
92.3
81.3
82.2
78.6
94.3
89.5
81
85.4
86.2
85.3
86.1
84.5
72.6
90
95.8
85.5
85.7
85.4
79.1
84.4
90
82.9
87.3
85.3
87.3
93.2
84.7
78
90.7
95
88.7
86.6
82.5
81.4
79.9
91.1
80.1
86.4
105.2
91.1
96.7
80.5
68.3
63.8
73.6
76.3
58.8
78
64.5
65.8
62.5
77.5
70
59.4
68.3
77.9
68.3
72
62.7
58
72.7
85.4
67.3
70.8
67.4
66
63.6
71.7
73.6
66.9
65.5
70.4
80.3
65
60.4
75.3
83.4
72.2
70.1
69.8
66.4
61.7
76.4
63.8
70.2
88.2
75.8
81.5
67.4
85.3
88.3
106.3
93.8
77.4
100.9
80.8
80.2
84.5
93.9
89.6
73.7
84
96
88
91.9
78.3
82.9
97.2
105.2
86.9
92.1
85.9
85
84.9
95.8
86.9
83.3
76.7
91.1
98
84.5
79.2
96.3
100.5
87.8
86.2
86.4
78.5
79.7
98.3
72.5
86.7
106.5
94.4
94.1
77.7
96.5
94
106.2
98.6
89.3
106.9
91.9
89.1
95.5
101.1
98.9
83.3
94
100.1
93.8
103.9
93.5
90.2
100.2
109.5
97.6
96.9
90.3
94.8
92.7
108.4
94.7
90.6
90.8
96.7
101.2
94.7
87
103.6
107.5
96.1
97.6
100.2
91.6
94.7
107
86.3
97.8
107.9
103.3
94.9
95.1
55.1
56.1
61.7
55.5
51.6
65.5
53.4
55.4
57.3
61.6
55
50.2
57.3
60.7
54.7
57.5
52.5
52.5
57.9
68.3
58.8
57.9
54.7
57.4
54.4
68.5
52.9
54.4
56.4
55.6
61.2
54.8
49.5
59.9
67.4
61.1
55.6
59
54.6
56.5
64.5
51.5
58.5
63.1
60.5
54.8
56.3
26
28.1
31.4
31.2
25.4
31.7
25.1
28.4
27.4
28.3
29.3
26.9
29.8
28.4
27.7
27.4
24.2
23.1
30.5
29.7
27.2
29.3
26.9
26.8
26.7
28.7
25
28.9
27.3
29.9
31
28.9
26.8
31.5
34.2
29.5
27.6
26.7
24.2
25.5
32.8
24.4
28.3
30.3
30.4
31.2
27
22.6
24
26.2
23
22.4
26.3
23.1
22.9
22.4
23
25
22.5
24.7
24.3
24.4
22.4
23.3
21
23.7
24.5
22.6
24.2
22.3
22.9
23.7
25.9
21
23.8
24.3
23.7
23.6
24.4
22.7
25.4
28.3
24.6
23.7
23.3
21.2
23.2
24.8
22
24.9
25.2
24.8
25.8
24.3
33.9
33.1
39.6
32.3
33.8
38.5
34.6
33.6
35.1
36.5
35.6
31.7
32.7
34.7
32.7
36.3
32.8
35.5
36.3
40.3
38.3
36.5
32.8
32.2
33.5
40.5
31.6
33.9
33.1
35.3
34.6
34.7
33.2
35.7
40.9
39.1
34.9
33.5
33
36.7
36.5
32
35.5
39.2
36.8
34.4
36.2
108.4
98.2
99.7
94.4
127.1
94.9
98.9
106.4
102.2
110.3
107.3
95
115.6
99.3
93.1
94.9
100
98.6
107.2
98.3
92.4
93
99.5
92.8
95.9
96.1
98.5
103.8
105
100.2
99.1
107.6
104
108.4
99.3
91.9
107.1
100.5
90.4
84.1
84.2
82.5
106.9
79.9
93
96.3
86.8
95.3
93
86.4
109
86.2
85.3
84.2
83.7
86.5
98.2
88
80.4
86
86.4
87.6
80.9
82.1
89.3
85.3
89
94.1
90.8
97
95.4
91.8
87.3
78.1
90.9
97.1
78.3
65.9
62.4
65.6
96.2
62.5
80.5
86.1
71.3
79.4
72.3
67.4
94.2
67
69.5
66.4
67.6
66.6
69.7
72
64.5
72.3
69.1
74.7
60.8
66.9
68.8
63.7
71.2
79.6
77.9
69.6
86
69.9
63.5
57.9
72.2
80.4
95.4
83.7
81.4
81.8
121.1
74
98.8
107.4
85.7
90.9
89
86.7
110.5
85.3
86.2
79.3
84.1
87.5
86
86
81.7
91.7
87.8
77
77.4
82.4
90.8
85.3
86.1
103.5
90.6
90.2
107.1
90.4
79.2
75.1
89.4
100.8
104.9
96.3
90.4
92.8
128.3
87.6
107.2
112
94
102.7
92
98.4
103.5
96.7
90.6
92
90.4
96.7
94.9
95.5
88.4
97.8
95.4
97.7
84.6
91.6
103.3
96.3
93.5
104.3
96.3
98.3
112.1
101
89.5
86.9
98.6
102.2
63.1
57
53.2
56.2
72.3
51.6
63
69.4
59.2
63
54.7
59.1
57.8
56.2
51.7
53.4
52.4
59.3
59.1
57.3
52.4
59.1
59.5
57
51
53.4
63
55.5
56.1
66.5
56.2
56.3
64.4
60.6
55.2
51.8
59
57.4
32.8
26.6
25.8
28.8
35.9
25.7
34.1
31.7
31.1
29.9
28.8
29.3
35.7
27
24.4
24.9
25.6
27.3
29.9
27.6
25.5
31
28.3
28.1
26.8
26.2
29.6
26.4
30.2
36.9
28.1
32
32.3
30.3
30.1
27.4
30.6
33.2
27
23.7
23
24.7
30.6
21.9
27.6
25.5
24.4
24.9
23.2
23.1
25.6
22.3
22.1
22.3
23
24
25
23.3
23
26.3
24.7
23.1
22.8
22.6
25.1
23
24.4
29
24.3
25.1
26.4
25.4
23.6
24
24.9
25.5
39.4
35.6
34.5
33
49
31.7
38.8
39.4
35.9
38.7
35
35.6
34.8
37
33.9
32.5
34.5
36
37.7
35.2
34.5
39.9
35.6
34.4
34.4
35
34.4
36.5
37
40.3
38.2
32.3
35.7
37.7
35.6
34.4
38.4
39.6
cal.gi
ank.gi
36.5
37.5
37.3
34.8
38.6
36.1
40.3
36.7
35
38.6
40.1
38.4
40
36
35
35.7
41.7
35.6
36.5
42
35.2
35.5
33.3
40.6
41.2
41.5
40
38.2
37.4
32.8
36.3
36.6
34.6
40.1
34.5
34.5
35.1
37.2
35.1
39.6
39.4
37.7
38.2
35.5
40
40.2
wri.gi
23.5
24.5
21.9
23
24.4
23.5
23.6
22.5
22
22.2
23.2
24.3
26
21.5
22
24
24.2
22
23
26.5
21
23
23.5
22.9
22.8
23.5
23.5
23.5
21.5
21
21
22.4
22.9
24.3
21.8
21.5
21
22.9
23
23.3
23.1
22.6
23.4
22.9
22.2
24.3
age
16.5
17
16.9
16.6
18
16.9
18.8
18
16.5
16.9
16.2
18.2
18
16.6
16.5
17.5
17.8
17.1
18.5
18.8
17.3
18
16
17
18.2
19
16.7
17.8
16.5
15.6
16.6
17.2
17
17.2
16.9
17
17
16
16.8
18.7
17.6
17.5
16.7
17
17.9
18.9
wgt
21
23
28
23
22
21
26
27
23
21
23
22
20
26
23
22
30
22
29
22
22
20
22
24
26
24
21
24
23
19
23
25
23
23
23
20
22
24
22
24
21
23
24
35
29
25
hgt
65.6
71.8
80.7
72.6
78.8
74.8
86.4
78.4
62
81.6
76.6
83.6
90
74.6
71
79.6
93.8
70
72.4
85.9
78.8
77.8
66.2
86.4
81.8
89.6
82.8
76.4
63.2
60.9
74.8
70
72.4
84.1
69.1
59.5
67.2
61.3
68.6
80.1
87.8
84.7
73.4
72.1
82.6
88.7
sex
174
175.3
193.5
186.5
187.2
181.5
184
184.5
175
184
180
177.8
192
176
174
184
192.7
171.5
173
176
176
180.5
172.7
176
173.5
178
180.3
180.3
164.5
173
183.5
175.5
188
189.2
172.8
170
182
170
177.8
184.2
186.7
171.4
172.7
175.3
180.3
182.9
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
37.9
40.1
36.1
33.6
38.1
36.5
38.3
38.6
30.5
36.3
34.7
39.1
42.4
35.2
37.5
38
36
33.8
36.2
34.5
36.3
37.4
39.6
32.6
39.1
35.6
39
36
34
37.9
37.6
35.1
35.6
39.5
41.2
40.8
35.8
35.7
36.4
38
36
38.6
36.5
37.9
35.2
37.8
35.2
23.2
25.7
21.4
20.3
21.1
22.7
23.4
21.9
19
20
21.1
23.2
25.3
21.4
21.6
22.4
21.8
21.1
22
22.8
21.8
22
24.6
21
24.5
21.6
21.2
23.8
22
22.7
21.1
20.1
22.1
23.6
23.3
25.9
21.3
22.1
20.7
21.6
22.6
23.1
21.9
22.3
22
20.3
21.1
16.8
17.7
16.3
15.8
16.9
17.9
17.3
16.4
15
15.8
15.3
17.7
17.5
16.5
16.1
17.2
17.5
16.9
17.5
17.4
16.7
17.2
17.7
16.1
17.9
16.6
15.6
17.5
17
15.8
15.8
15.4
16.3
18
16
18
16.5
16.7
16.2
16.6
17.3
17.3
16.4
16.6
17
16.5
16.3
23
20
25
29
23
23
36
25
24
20
52
50
46
51
28
48
35
23
23
62
21
26
33
36
41
40
27
27
23
31
26
23
24
24
34
21
25
34
31
40
21
33
25
29
27
44
26
84.1
94.1
74.9
59.1
75.6
86.2
75.3
87.1
55.2
57
61.4
76.8
86.8
72.2
71.6
84.8
68.2
66.1
72
64.6
74.8
70
101.6
63.2
79.1
78.9
67.7
66
68.2
63.9
72
56.8
74.5
90.9
93
80.9
72.7
68
70.9
72.5
72.5
83.4
75.5
73
70.2
73.4
70.5
188
177.2
172.1
167
169.5
174
172.7
182.2
164.1
163
171.5
184.2
174
174
177
186
167
171.8
182
167
177.8
164.5
192
175.5
171.2
181.6
167.4
181.1
177
174.5
177.5
170.5
182.4
197.1
180.1
175.5
180.6
184.4
175.5
180.6
177
177.1
181.6
176.5
175
174
165.1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
38.6
39.3
37.7
35.3
35.5
39.4
43
41.8
38.5
32.5
35
34.5
34
39.7
37.3
34.2
34.3
35.5
34.7
33.5
39.4
38.3
30.2
37.7
39.4
38.2
32.1
38.3
39.6
34.6
47.7
35.8
35.9
37
40
37.7
39
36.4
37.7
39.3
40.7
32.9
36.8
33
36.6
36.2
37.7
21.2
24.6
22.7
21.5
24
23.2
25.3
24
22.5
21.2
21
20.9
20.8
26.3
23.1
21.3
22.3
23
23
23
25.6
23.7
16.4
24.5
25.1
22.8
20
24.6
25.8
20.6
27
22.2
23
27.5
24.2
21.6
25.8
23.2
23.4
24.5
25.3
23.2
24.6
23
22.9
21.2
23.6
16
18.6
16.2
16.2
16.5
17
17.7
17.8
17.5
14.6
16.4
16
16.4
18.1
16.7
15.6
18.4
16.3
16.1
17.1
18.3
18
16.1
17.3
17.7
18.2
15.3
18.1
17.6
16
19.2
16.3
17.4
17.9
17.6
18.3
19.5
16.3
17
17.1
17.5
17
18.4
16.8
18.1
16.2
18.5
22
37
38
20
21
24
45
25
22
29
37
20
20
32
23
25
27
21
27
25
38
44
27
37
28
33
25
21
30
26
27
33
29
27
34
42
29
41
43
43
29
27
62
33
45
30
20
68.9
102.3
68.4
65.9
75.7
84.5
87.7
86.4
73.2
53.9
72
55.5
58.4
83.2
72.7
64.1
72.3
65
86.4
65
88.6
84.1
66.8
75.5
93.2
82.7
58
79.5
78.6
71.8
116.4
72.2
83.6
85.5
90.9
85.9
89.1
75
77.7
86.4
90.9
73.6
76.4
69.1
84.5
64.5
69.1
177
192
176.5
169.4
182.1
179.8
175.3
184.9
177.3
167.4
178.1
168.9
157.2
180.3
170.2
177.8
172.7
165.1
186.7
165.1
174
175.3
185.4
177.8
180.3
180.3
177.8
177.8
177.8
177.8
177.8
163.8
188
198.1
175.3
166.4
190.5
166.4
177.8
179.7
172.7
190.5
185.4
168.9
167.6
175.3
170.2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
39.6
41.8
37.6
39.2
40
37.7
36.4
33
38.4
37.7
36.9
33.1
37.3
37
40.8
34.4
34
37.4
39.7
35.5
40.8
37.8
42.1
37.8
35
41.2
39.3
36
42.1
36.2
36.8
38.2
37
36.4
42.6
41.8
37.4
32.3
38.8
36.5
35.1
38.5
37.6
38.9
39.5
37.9
36.7
24.7
25
25
24.9
23.7
24.5
22.9
22
21.3
23.8
23
22.1
22.7
22.5
24.6
20
22
23
25.4
23.1
24.8
24.9
26.1
24
21
27.7
23.5
21.6
26.4
22.8
23.2
23.8
23.7
22.8
25.8
29.3
22.6
22
26.4
24.3
21.8
24.5
23
24.2
24.4
23.9
24.3
18.2
19.6
17.7
17.6
18.1
17.1
17
15.5
16.4
17.1
18
16.3
16.8
17.4
17.1
16.5
17
16.4
18.4
16.3
17.1
17.9
19.5
17.3
16.6
18.1
16.8
17.3
17.9
17.3
16.5
18.2
18.3
15.9
18.8
18
17.1
17.1
18.1
18.7
16.3
17.3
17.5
17.9
16.8
17.1
17.7
22
51
34
44
46
34
32
28
31
29
42
29
31
30
27
25
24
33
45
37
44
34
55
43
24
22
38
24
29
25
37
30
26
35
29
30
37
34
28
27
32
28
22
44
25
49
54
108.6
86.4
80.9
87.7
94.5
80.2
72
71.4
72.7
84.1
76.8
63.6
80.9
80.9
85.5
68.6
67.7
66.4
102.3
70.5
95.9
84.1
87.3
71.8
65.9
95.9
91.4
81.8
96.8
69.1
82.7
75.5
79.5
73.6
91.8
84.1
85.9
81.8
82.5
80.5
70
81.8
84.1
90.5
91.4
89.1
85
190.5
177.8
190.5
177.8
184.2
176.5
177.8
180.3
171.4
172.7
172.7
177.8
177.8
182.9
170.2
167.6
175.3
165.1
185.4
181.6
172.7
190.5
179.1
175.3
170.2
193
171.4
177.8
177.8
167.6
167.6
180.3
182.9
176.5
186.7
188
188
177.8
174
177.8
171.4
185.4
185.4
188
188
182.9
176.5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
33.4
36.5
36.3
36.6
34.8
32.6
36.6
41.2
35
37
39.2
37.3
34.1
32.3
38.5
34
36.9
39.2
37
35
38.4
37
38.5
42
38.7
43.6
32.7
41.8
36.3
37.1
41.5
38.1
38.3
37.4
28.9
34.4
39.4
39.6
34.8
36
37.5
37
38.1
36
33.6
32.8
37.9
21.2
23.7
22
22.6
22
22
22.7
25.7
23.5
25.6
25.7
24.3
21.7
23
24.3
22
21.3
23
22
22.4
22.9
21.8
24
23.6
25.7
26.9
22.5
26.2
23.4
23.7
27.7
25.3
25.2
24.1
20.3
24.5
22.6
25.5
22.5
21.3
23.3
22.7
23
23.5
22.1
21.4
22.5
16.7
17.5
17.7
17.5
18.1
16.4
16.4
18.8
17.1
17.9
15.9
17.2
17.1
16.2
17.4
17
16.6
17.5
17.2
16.7
17.9
17.5
17
17.5
17.1
17
17.9
17.8
16.7
16.6
18.1
17.7
17.4
17.1
15.8
17.1
17.5
18.9
16.4
15.1
16.7
16.6
17
18.1
17.1
16.3
17.8
49
60
42
52
23
33
46
43
56
21
18
21
45
22
55
42
29
40
24
62
26
35
37
34
25
30
32
27
42
44
46
19
43
28
39
30
36
48
48
53
45
39
43
65
45
37
55
69.1
73.6
80.5
82.7
86.4
67.7
92.7
93.6
70.9
75
93.2
93.2
77.7
61.4
94.1
75
83.6
85.5
73.9
66.8
87.3
72.3
88.6
75.5
101.4
91.1
67.3
77.7
81.8
75.5
84.5
76.6
85
102.5
77.3
71.8
87.9
94.3
70.9
64.5
77.3
72.3
87.3
80
82.3
73.6
74.1
175.3
175.3
188
188
175.3
170.5
179.1
177.8
175.3
182.9
170.8
188
180.3
177.8
185.4
168.9
185.4
180.3
174
167.6
182.9
160
180.3
167.6
186.7
175.3
175.3
175.9
175.3
179.1
181.6
177.8
182.9
177.8
184.2
179.1
176.5
188
174
167.6
170.2
167.6
188
174
176.5
180.3
167.6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
36.8
34.3
35.9
34.9
38.3
38.8
33.4
37.3
34.3
37
39.8
42
39.6
32.2
38.5
32.5
36.7
33.3
35
32
38
37.4
35.8
32.5
34.5
35.3
30.4
32.8
35
29.6
38.6
33
36.5
31.5
38.6
30.9
40
40
33.7
36
38.4
36.7
33
31.5
35
38.9
34.8
23.4
23.3
22.6
23.7
25.5
25.1
23.1
23.5
21.1
24.3
25.4
27.7
25.2
21
22.5
19
23
19.9
23
19
22
21.6
22.6
19.9
20.5
20.9
17.9
19.1
21
18.5
23.8
19
20.6
22
23
19.4
24.2
23
20.9
21
21.3
21.3
20.5
20.5
20.1
23.3
20.5
19.6
17.3
17.3
18.4
19.4
18.9
18.3
17.3
16.3
16.7
18.1
18.4
17
13.5
15
14
15
14.5
14.5
13.9
16.8
15.2
16.3
13.8
15.3
14.4
13.2
13.8
14
14.5
17
13.2
15.9
13.8
16.6
14.5
17.6
16
15.2
15
15.6
15.6
14.5
14
14.9
15.9
14.4
33
25
35
28
26
43
30
26
51
30
24
35
37
22
20
19
25
21
23
26
22
28
40
32
25
25
29
22
25
23
37
19
23
25
26
24
29
22
30
23
38
23
19
46
20
22
25
85.9
73.2
76.3
65.9
90.9
89.1
62.3
82.7
79.1
98.2
84.1
83.2
83.2
51.6
59
49.2
63
53.6
59
47.6
69.8
66.8
75.2
55.2
54.2
62.5
42
50
49.8
49.2
73.2
47.8
68.8
50.6
82.5
57.2
87.8
72.8
54.5
59.8
67.3
67.8
47
46.2
55
83
54.4
188
180.3
167.6
183
183
179.1
170.2
177.8
179.1
190.5
177.8
180.3
180.3
161.2
167.5
159.5
157
155.8
170
159.1
166
176.2
160.2
172.5
170.9
172.9
153.4
160
147.2
168.2
175
157
167.6
159.5
175
166.8
176.5
170.2
174
173
179.9
170.5
160
154.4
162
176.5
160
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
31
33.4
35.2
35.3
38
33.4
34.6
36.3
30
31.6
35.7
35.4
35.6
32.9
36.3
37.1
34
36
35.4
33.8
34
35.8
32.5
37.1
33.5
34.2
33.3
37.7
34.2
39.7
41.1
31.5
34.8
37.8
35
33.7
32.4
31.3
32.1
38.5
38.2
35.5
34.4
30.3
35.2
38.1
40.4
20
20
22.3
21.2
21.5
21.9
20
20.6
18.8
18.9
22
21.2
21
19.8
21.4
21.9
20.7
21
20.7
20.7
20.3
20.7
19.7
20.1
20
21.5
19.6
21.7
20.6
24.3
22.9
18.9
20.9
20.7
22.1
19.1
19
18.4
19.7
21.3
21.8
21
20.3
20.2
23.2
21.8
23.3
14
15.6
16.1
14.6
15.3
15.2
15.1
15.2
14.3
15
15.1
15.7
14.7
13.8
15.3
14.3
15.5
14.6
15.5
14.6
14.6
14.4
14.6
14.9
14.6
15.1
15.3
15.9
15
15.9
16.4
14.1
14.3
16.6
15.6
14.7
14.2
14.7
15
15.4
15.9
15
14.4
15
16.2
16.2
16.4
21
23
31
29
19
21
23
24
20
19
20
19
20
19
22
39
18
19
26
20
20
26
21
21
38
23
37
19
25
20
41
26
21
47
19
44
35
32
46
22
49
52
25
48
41
18
30
45.8
53.6
73.2
52.1
67.9
56.6
62.3
58.5
54.5
50.2
60.3
58.3
56.2
50.2
72.9
59.8
61
69.1
55.9
46.5
54.3
54.8
60.7
60
62
60.3
52.7
74.3
62
73.1
80
54.7
53.2
75.7
61.1
55.7
48.7
52.3
50
59.3
62.5
55.7
54.8
45.9
70.6
67.2
69.4
152
162.1
170
160.2
161.3
166.4
168.9
163.8
167.6
160
161.3
167.6
165.1
160
170
157.5
167.6
160.7
163.2
152.4
157.5
168.3
180.3
165.5
165
164.5
156
160
163
165.7
161
162
166
174
172.7
167.6
151.1
164.5
163.5
152
169
164
161.2
155
170
176.2
170
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35.2
35
36.7
34.8
36.2
33.9
32.6
36.4
34.8
34.3
35.4
35.4
33
33
32.5
34.3
35.3
39
34
35.2
39.8
32.2
36.6
35.9
36.6
39.4
35.8
37
37
34
45
34.2
37.4
35.6
33
38.4
33.2
28.4
35.8
33
37.6
32
33.5
33
35.1
31.5
37.2
21.6
22.2
21.8
20.2
22.1
21.4
19.1
21.8
21
21.7
22.2
21.8
19.6
19.4
21
21.5
21.6
23.2
20.4
20.4
22
19
22
19.9
23.8
23.2
20.8
21.8
23
21.3
25.8
20.3
22
21
20
23.2
20.5
17.4
21.2
20.7
22.4
20.1
21.8
20.2
21.6
18.9
21.5
14.6
16.2
16.2
14.4
15.8
14.4
14
15.6
15
14.8
15.6
15.4
14
14.2
14.8
15
15.6
16.2
15.4
14.4
14.4
14.6
15.1
14.6
15.3
15.8
15.5
15.8
16
15.2
18.2
14.2
16
14.5
14
15.8
15
13.2
15.2
14.4
16.6
13.1
16
14.9
15.6
13.4
15.8
20
24
23
30
23
45
20
20
23
21
28
45
24
25
19
20
29
24
24
25
31
22
20
32
25
19
23
22
20
27
34
25
26
19
26
25
20
21
18
19
27
26
36
20
28
32
32
58.2
64.8
71.6
52.8
59.8
49
50
69.2
55.9
63.4
58.2
58.6
45.7
52.2
48.6
57.8
55.6
66.8
59.4
53.6
73.2
53.4
69
58.4
56.2
70.6
59.8
72
65.2
56.6
105.2
51.8
63.4
59
47.6
63
55.2
45
54
50.2
60.2
44.8
58.8
56.4
62
49.2
67.2
162.5
170.3
164.1
169.5
163.2
154.5
159.8
173.2
170
161.4
169
166.2
159.4
162.5
159
162.8
159
179.8
162.9
161
151.1
168.2
168.9
173.2
171.8
178
164.3
163
168.5
166.8
172.7
163.5
169.4
167.8
159.5
167.6
161.2
160
163.2
162.2
161.3
149.5
157.5
163.2
172.7
155
156.5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
35
34.4
34
34.4
33.7
29.6
33.5
31.6
38.2
31.2
35
32.8
35.5
34.5
36.9
33
33.8
37.4
34.8
30.5
35.7
36.6
34
32.3
33.1
32.9
41.9
33.4
32.7
33.5
35.6
38.6
34.6
33.1
35.4
38
35.8
37
33.3
38.5
32.1
34.6
32.6
35.5
36.4
33.7
34.3
21
21.3
19.8
20
22
18.6
21.1
18.8
20.4
20.4
21.7
19
22
21.4
20.4
19.4
20.6
20.6
20.3
20.1
23.8
20.7
20.9
20.4
19.9
20.3
24.3
21.5
18.8
21
23.5
22.3
21.2
21.9
20.3
21
20.1
22.5
21.2
22.2
21
21.5
19.9
22.6
24.5
21.6
21
14.8
14.6
13.8
15
14.6
13.8
15.3
14.2
14.4
14.4
16
13.9
15.5
15.2
15.7
14.5
14.8
14.8
13.4
14.6
14.1
15.6
14.2
14.7
15
14.6
15.4
14.5
14.7
15.1
14.7
17.3
14.1
15.1
14.6
14.6
14.6
15.1
14.9
16
15
14.6
13.7
15.4
16
15.5
14.4
23
20
20
20
23
20
28
23
19
28
19
29
32
20
28
36
22
20
22
32
40
40
42
40
44
30
28
37
40
45
35
41
27
20
24
36
27
32
64
21
32
35
41
40
29
40
24
53.8
54.4
58
59.8
54.8
43.2
60.5
46.4
64.4
48.8
62.2
55.5
57.8
54.6
59.2
52.7
53.2
64.5
51.8
56
63.6
63.2
59.5
56.8
64.1
50
72.3
55
55.9
60.4
69.1
84.5
55.9
55.5
69.5
76.4
61.4
65.9
58.6
66.8
56.6
58.6
55.9
59.1
81.8
70.7
56.8
164
160.9
162.8
167
160
160
168.9
158.2
156
160
167.1
158
167.6
156
162.1
173.4
159.8
170.5
159.2
157.5
161.3
162.6
160
168.9
165.1
162.6
165.1
166.4
160
152.4
170.2
162.6
170.2
158.8
172.7
167.6
162.6
167.6
156.2
175.2
172.1
162.6
160
165.1
182.9
166.4
165.1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
33.7
35.2
39.1
31.3
32.4
39.7
32.7
35
35.7
34.6
36.6
30.7
34.3
34.5
33
37.9
36.1
36.4
34.3
37
35.6
35.3
29.5
32.6
33.6
39.5
30.2
33.9
35
33.8
35.6
34.8
31.5
35.8
41.2
38.7
32
33.1
34.3
36.2
36.2
32.6
36.3
38.4
35.9
37.3
36.7
21.8
22.1
24.8
20.3
21
22.8
21.4
19.7
20.4
21.9
22.5
20.5
21.7
20.9
19.6
23.4
22
20.3
20.5
22.4
21
20.3
18.7
19.2
20.2
23.3
19.3
20.8
20.7
23
20
22.5
18.8
21.1
23.4
26
21.1
19.6
20.2
22
23.9
21
21.4
23.1
21.8
21.8
23.7
15
16
16.2
15.1
14.8
15.6
14.6
14.8
14.8
14.7
16.4
15.2
15.4
14.9
14.9
14.5
14.8
13
14.8
15.3
14.6
15.4
13.7
14.6
14.6
15.6
13.6
15.5
14.2
16.3
14.3
15.3
14.7
16.3
15.6
15.5
15.3
14.2
15
14.8
15.5
14
15.3
16.4
15.5
14.6
15.9
23
41
44
53
19
24
25
20
34
32
24
29
31
34
36
32
39
37
52
24
33
42
34
37
39
41
36
19
22
23
36
45
25
67
26
21
33
25
24
21
35
27
27
26
25
44
29
60
58.2
72.7
54.1
49.1
75.9
55
57.3
55
65.5
65.5
48.6
58.6
63.6
55.2
62.7
56.6
53.9
63.2
73.6
62
63.6
53.2
53.4
55
70.5
54.5
54.5
55.9
59
63.6
54.5
47.3
67.7
80.9
70.5
60.9
63.6
54.5
59.1
70.5
52.7
62.7
86.3
66.4
67.3
63
177.8
165.1
175.3
154.9
158.8
172.7
168.9
161.3
167.6
165.1
175.3
157.5
163.8
167.6
165.1
165.1
168.9
162.6
164.5
176.5
168.9
175.3
159.4
160
170.2
162.6
167.6
162.6
160.7
160
157.5
162.6
152.4
170.2
165.1
172.7
165.1
170.2
170.2
170.2
161.3
167.6
167.6
165.1
162.6
152.4
168.9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
39.1
34
31
34.6
45.4
34.7
38.2
38.7
34.4
36.3
34.2
37.4
35.5
33
30.8
31.7
32.5
34.9
37.7
31.9
32.7
39.7
34.6
32.7
33.1
35.2
35
34.1
37.5
37.9
36.6
33.8
37
37.9
33.3
34.1
36.6
35.9
23
21.7
19.2
21.7
24.1
18.5
22.2
23.7
21.2
21.3
20.5
22.5
19.5
21.6
19.9
21.7
21.7
21.4
23.7
19.6
20.3
21.6
23
20.9
21
22.4
21
21.3
22.6
24.6
22.3
20.8
21.4
22.4
22.4
21.2
22
23
16.5
15.1
14.7
15.8
17.8
13.9
16.3
16.3
14.2
15.5
14.8
14.4
15
15
14.1
13.4
14.6
14.6
16.2
15.4
14.9
15.4
16.6
15.2
15.4
15.2
15.9
15
15.7
16.4
15.4
15.9
15.8
15.4
15.2
15.5
15.5
16.4
26
23
32
32
43
32
41
33
28
28
25
38
37
25
37
27
27
20
19
32
26
56
23
19
31
34
34
24
22
34
30
32
40
29
21
33
33
38
73.6
62.3
57.7
55.4
104.1
55.5
77.3
80.5
64.5
72.3
61.4
58.2
81.8
63.6
53.4
54.5
53.6
60
73.6
61.4
55.5
63.6
60.9
60
46.8
57.3
64.1
63.6
67.3
75.5
68.2
61.4
76.8
71.8
55.5
48.6
66.4
67.3
170.2
175.2
175.2
160
165.1
174
170.2
160
167.6
167.6
167.6
154.9
162.6
175.3
171.4
157.5
165.1
160
174
162.6
174
162.6
161.3
156.2
149.9
169.5
160
175.3
169.5
160
172.7
162.6
157.5
176.5
164.4
160.7
174
163.8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Fema l e Hei ght
wgt
51.6
59
49.2
63
53.6
59
47.6
69.8
66.8
75.2
55.2
hgt
147.2
149.5
149.9
151.1
151.1
152.0
152.0
152.4
152.4
152.4
152.4
54.2
62.5
42
50
49.8
49.2
153.4
154.4
154.5
154.9
154.9
155.0
73.2
47.8
68.8
50.6
82.5
57.2
87.8
72.8
54.5
59.8
67.3
67.8
47
46.2
55
83
54.4
45.8
53.6
73.2
52.1
67.9
56.6
62.3
58.5
54.5
50.2
60.3
58.3
56.2
50.2
72.9
59.8
61
69.1
155.0
155.8
156.0
156.0
156.0
156.2
156.2
156.5
157.0
157.0
157.5
157.5
157.5
157.5
157.5
157.5
157.5
157.5
158.0
158.2
158.8
158.8
159.0
159.0
159.1
159.2
159.4
159.4
159.5
159.5
159.5
159.8
159.8
160.0
160.0
55.9
46.5
54.3
54.8
60.7
60
62
60.3
52.7
74.3
62
73.1
80
54.7
53.2
75.7
61.1
55.7
48.7
52.3
50
59.3
62.5
55.7
54.8
45.9
70.6
67.2
69.4
58.2
64.8
71.6
52.8
59.8
49
50
69.2
55.9
63.4
58.2
58.6
45.7
52.2
48.6
57.8
55.6
66.8
59.4
53.6
73.2
53.4
69
58.4
56.2
70.6
59.8
72
65.2
56.6
105.2
51.8
63.4
59
47.6
63
55.2
45
54
50.2
60.2
44.8
58.8
56.4
62
49.2
67.2
53.8
54.4
58
59.8
54.8
43.2
60.5
46.4
64.4
48.8
62.2
55.5
57.8
54.6
59.2
52.7
53.2
64.5
51.8
56
63.6
63.2
59.5
56.8
64.1
50
72.3
55
55.9
60.4
69.1
84.5
55.9
55.5
69.5
76.4
61.4
65.9
58.6
66.8
56.6
58.6
55.9
59.1
81.8
70.7
56.8
60
58.2
72.7
54.1
49.1
75.9
55
57.3
55
65.5
65.5
48.6
58.6
63.6
55.2
62.7
56.6
53.9
63.2
73.6
62
63.6
53.2
53.4
55
70.5
54.5
54.5
55.9
59
63.6
54.5
47.3
67.7
80.9
70.5
60.9
63.6
54.5
59.1
70.5
52.7
62.7
86.3
66.4
67.3
63
73.6
62.3
57.7
55.4
104.1
55.5
77.3
80.5
64.5
72.3
61.4
58.2
81.8
63.6
53.4
54.5
53.6
60
73.6
61.4
55.5
63.6
60.9
60
46.8
57.3
64.1
63.6
67.3
75.5
68.2
61.4
76.8
71.8
55.5
48.6
66.4
67.3
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.0
160.2
160.2
160.7
160.7
160.7
160.9
161.0
161.0
161.2
161.2
161.2
161.3
161.3
161.3
161.3
161.3
161.3
161.3
161.4
162.0
162.0
162.1
162.1
162.2
162.5
162.5
162.6
162.6
162.6
162.6
162.6
162.6
162.6
162.6
162.6
162.6
162.6
162.6
162.6
162.6
162.8
162.8
162.9
163.0
163.0
163.2
163.2
163.2
163.2
163.5
163.5
163.8
163.8
163.8
164.0
164.0
164.1
164.3
164.4
164.5
164.5
164.5
165.0
165.1
165.1
165.1
165.1
165.1
165.1
165.1
165.1
165.1
165.1
165.1
165.1
165.1
165.1
165.5
165.7
166.0
166.0
166.2
166.4
166.4
166.4
166.8
166.8
167.0
167.1
167.5
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.6
167.8
168.2
168.2
168.3
168.5
168.9
168.9
168.9
168.9
168.9
168.9
168.9
168.9
169.0
169.0
169.4
169.5
169.5
169.5
170.0
170.0
170.0
170.0
170.0
170.0
170.2
170.2
170.2
170.2
170.2
170.2
170.2
170.2
170.2
170.2
170.3
170.5
170.5
170.9
171.4
171.8
172.1
172.5
172.7
172.7
172.7
172.7
172.7
172.7
172.7
172.9
173.0
173.2
173.2
173.4
174.0
174.0
174.0
174.0
174.0
174.0
175.0
175.0
175.2
175.2
175.2
175.3
175.3
175.3
175.3
175.3
176.2
176.2
176.5
176.5
176.5
176.5
177.8
178.0
179.8
179.9
180.3
182.9
Thi s col umns of fema l e wei ghts
a nd hei ghts were copi ed a nd
pa s ted from s orti ng the da ta i nto
ma l e a nd fema l e a nd then jus t
copyi ng a nd pa s ti ng the fema l e
hei ghts . Get the Des cri pti ve
hgt
Mea n
Sta nda rd Error
Medi a n
Mode
Sta nda rd Devi a ti on
Sa mpl e Va ri a nce
Kurtos i s
Skewnes s
Ra nge
Mi ni mum
Ma xi mum
Sum
Count
164.8723077
0.405878994
164.5
160
6.544602131
42.83181705
-0.281127467
0.06612134
35.7
147.2
182.9
42866.8
260
Exercises 1 and 2: Here is the histogram for female heights, plotted as frequency counts. This is the default histogram
made using the Histogram option on the insert chart menu. This used 10 bins (classes) and the width of each is 3.6. Try
using Excel’s built-in Histogram function to create a similar histogram. Right click on the x-axis and select format axis then
edit the number of bins to be 7 or 8.
Click on the little plus symbol on the edge of the chart (mouse over it) and click to include data labels. The default will
show the labels as in the example here. Click into those settings to explore more options as desired. Once you have it
done here, do it also for the male height data for further practice.
As done in the textbook and the homework assignments, compare the shape of the data distribution to that of a Normal
bell curve shaped distribution of values. Although Excel does the histogram nicely, it does not have a built in feature to
overlay a Normal curve for easy comparison. Likewise, Excel can be used to create the Normal Q-Q plots, but not via a
built-in feature. Normal distribution assessment via the normal distribution overlay on histograms and Q-Q plots is being
simplified with the use of an online calculator running an R script (link is below).
First select the data column (use click on first data value and then use Crtl+Shift+down arrow or any other method to
select all the data values) copy these and then go to the website. There will be default example data there, select this
data and delete it then paste the female height data–if there is an extra space at the bottom then click the backspace to
delete the extra empty row. Edit the titles as desired then click Compute. Scroll to review the charts. Right click the charts
to get the copy option, paste into your lab file. Reminder: If using such a site to generate charts for reports it will need a
citation, scroll more to see the citation information for this site (not needed for this lab, but keep in mind for work or use
for any reports in your capstone courses).
Once you have the charts, refer to Chapter 3 sections 1 and 2 for more on how to interpret these. Discuss this in the
online discussion as needed. In general you should use the descriptive statistics and the graphics to describe the center,
shape and spread of the data values (several sentences).
Cl i ck to go to https ://www.wes s a .net/rwa s p_fi tdi s trnorm.wa s p
Optional:
For those more comfortable with Excel. Please manage your time and use the website above if time does not allow for exploringthis in Excel.
This can be done in Excel; use the values of the midpoint of each bin as the x values, compute the normal density function value using
=NORM.DIST(midpoint,164.9,6.5,FALSE) click the first bin midpoint (x value) and Excel inserts the cell reference, this way you can copy the formula down
the column like you did in previous Excel labs. Now you should have a table as shown with columns: midpoints, normal densityfunction, frequency and
relative frequency for female heights.
Once you have graphed the histogram, now right click the chart and click the option select data to add in the other x and y cell ranges. Once added, edit
this to be a scatterplot line with smooth lines showing (and no point dots) and you will have a histogram for female heights with the corresponding
normal distribution on the same graph. When on the same graph, there is one more step, click on the bars or line and select secondary axis to have the
two graphs plotted on their own y axis, but same x axis. If you have issues then plot them separately and place side by side for comparison. Alternately,
select the table of bin midpoints through relative frequencies and insert a scatterplot as shown. In the option on the side,unselect the other y options to
show just the normal density and the relative frequency counts. Right click on one of these lines and select “Format Data Series” and then click the
option to use a secondary axis, this should now show the shapes for easy comparison.
Norma l Dens i ty
Bi n Mi dpoi nts (x)
Functi on (y)
149
0.00308
152.6
0.01024
156.2
0.02506
159.8
0.04511
163.4
0.05976
167
0.05825
170.6
0.04178
174.2
0.02205
177.8
0.00856
181.4
0.00245
Rel a ti ve
Frequen
0.25000
cy
(freque
ncy
0.20000
Frequency Counts count
(rea d off from
di vi ded
cha rt) (y)
by tota l ) 0.15000
3
0.01154
9
0.03462
0.10000
24
0.09231
53
0.20385
58
0.22308 0.05000
35
0.13462
37
0.14231
29
0.11154 0.00000
140
8
0.03077
4
0.01538
260
Qui ck a ri thmeti c to veri fy correct count
Chart Title
0.07000
0.06000
0.05000
0.04000
0.03000
0.02000
0.01000
0.00000
145
ccd6ddee64a 660425769c01e046ddb52
150
155
160
165
170
175
180
Relative Frequency (frequency count divided by total) (y)
Normal Density Function (y)
185
wgt
hgt
65.6
71.8
80.7
72.6
78.8
74.8
86.4
78.4
62
81.6
76.6
83.6
90
74.6
71
79.6
93.8
70
72.4
85.9
78.8
77.8
66.2
86.4
81.8
89.6
82.8
76.4
63.2
60.9
74.8
70
72.4
84.1
69.1
59.5
67.2
61.3
68.6
80.1
87.8
174
175.3
193.5
186.5
187.2
181.5
184
184.5
175
184
180
177.8
192
176
174
184
192.7
171.5
173
176
176
180.5
172.7
176
173.5
178
180.3
180.3
164.5
173
183.5
175.5
188
189.2
172.8
170
182
170
177.8
184.2
186.7
Complete exercises 1 and 2, try the female height
analysis first because you have this one completed as an
example in the previous sheet, be sure that you are
getting it to match before moving on to male height
data. Practice with this and discuss in the online
discussion or work with a tutor as needed.
The charts made in the
https://www.wessa.net/rwasp_fitdistrnorm.wasp can
be copied and pasted into Excel or Word documents.
Tip: Make an Excel histogram as a double check and for
practice.
84.7
73.4
72.1
82.6
88.7
84.1
94.1
74.9
59.1
75.6
86.2
75.3
87.1
55.2
57
61.4
76.8
86.8
72.2
71.6
84.8
68.2
66.1
72
64.6
74.8
70
101.6
63.2
79.1
78.9
67.7
66
68.2
63.9
72
56.8
74.5
90.9
93
80.9
72.7
68
70.9
72.5
72.5
83.4
171.4
172.7
175.3
180.3
182.9
188
177.2
172.1
167
169.5
174
172.7
182.2
164.1
163
171.5
184.2
174
174
177
186
167
171.8
182
167
177.8
164.5
192
175.5
171.2
181.6
167.4
181.1
177
174.5
177.5
170.5
182.4
197.1
180.1
175.5
180.6
184.4
175.5
180.6
177
177.1
75.5
73
70.2
73.4
70.5
68.9
102.3
68.4
65.9
75.7
84.5
87.7
86.4
73.2
53.9
72
55.5
58.4
83.2
72.7
64.1
72.3
65
86.4
65
88.6
84.1
66.8
75.5
93.2
82.7
58
79.5
78.6
71.8
116.4
72.2
83.6
85.5
90.9
85.9
89.1
75
77.7
86.4
90.9
73.6
181.6
176.5
175
174
165.1
177
192
176.5
169.4
182.1
179.8
175.3
184.9
177.3
167.4
178.1
168.9
157.2
180.3
170.2
177.8
172.7
165.1
186.7
165.1
174
175.3
185.4
177.8
180.3
180.3
177.8
177.8
177.8
177.8
177.8
163.8
188
198.1
175.3
166.4
190.5
166.4
177.8
179.7
172.7
190.5
76.4
69.1
84.5
64.5
69.1
108.6
86.4
80.9
87.7
94.5
80.2
72
71.4
72.7
84.1
76.8
63.6
80.9
80.9
85.5
68.6
67.7
66.4
102.3
70.5
95.9
84.1
87.3
71.8
65.9
95.9
91.4
81.8
96.8
69.1
82.7
75.5
79.5
73.6
91.8
84.1
85.9
81.8
82.5
80.5
70
81.8
185.4
168.9
167.6
175.3
170.2
190.5
177.8
190.5
177.8
184.2
176.5
177.8
180.3
171.4
172.7
172.7
177.8
177.8
182.9
170.2
167.6
175.3
165.1
185.4
181.6
172.7
190.5
179.1
175.3
170.2
193
171.4
177.8
177.8
167.6
167.6
180.3
182.9
176.5
186.7
188
188
177.8
174
177.8
171.4
185.4
84.1
90.5
91.4
89.1
85
69.1
73.6
80.5
82.7
86.4
67.7
92.7
93.6
70.9
75
93.2
93.2
77.7
61.4
94.1
75
83.6
85.5
73.9
66.8
87.3
72.3
88.6
75.5
101.4
91.1
67.3
77.7
81.8
75.5
84.5
76.6
85
102.5
77.3
71.8
87.9
94.3
70.9
64.5
77.3
72.3
185.4
188
188
182.9
176.5
175.3
175.3
188
188
175.3
170.5
179.1
177.8
175.3
182.9
170.8
188
180.3
177.8
185.4
168.9
185.4
180.3
174
167.6
182.9
160
180.3
167.6
186.7
175.3
175.3
175.9
175.3
179.1
181.6
177.8
182.9
177.8
184.2
179.1
176.5
188
174
167.6
170.2
167.6
87.3
80
82.3
73.6
74.1
85.9
73.2
76.3
65.9
90.9
89.1
62.3
82.7
79.1
98.2
84.1
83.2
83.2
188
174
176.5
180.3
167.6
188
180.3
167.6
183
183
179.1
170.2
177.8
179.1
190.5
177.8
180.3
180.3
nba Heights QQ Plot Example
Data: Height
(inches)
sorted min to
max
69
70
70
71
71
72
72
72
72
72
72
72
72
72
72
72
72
72
73
73
73
73
73
73
73
73
73
73
73
73
73
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
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75
75
75
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75
75
75
75
75
75
75
75
75
75
75
75
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Q-Q plot to assess normality:
This is another example to
accompany the female and male
data that you assessed. This
example can be done again for
practice and discussed in the
discussion.
Histogram shows a slightly
longer left tail. This is
consistent with the small
negative skewness value in
the descriptive statistics
and slight deviation from
the line in the normal plot.
Copy the data values and paste
them into the online analysis
tool at
https://www.wessa.net/rwasp_fi
tdistrnorm.wasp
Data: Height (inches) sorted min to max
Mean
79.209
Standard Error
0.1713
Median
80
Mode
81
Standard Deviation 3.5734
Sample Variance
12.77
Kurtosis
-0.4861
Skewness
-0.3686
Range
21
Minimum
69
Maximum
90
Sum
34456
Count
435
ccd6ddee64a660425769c01e046ddb52
Skewness is close to zero,
so the distribution of nba
heights is slightly left
skewed.
Normal probabilities
Okay, so now we have some tools to judge whether or not a variable is normally distributed. Why
should we care? It turns out that statisticians know a lot about the normal distribution. Once we
decide that a random variable is approximately normal, we can answer all sorts of questions about
that variable related to probability. Take, for example, the question of, “What is the probability
that a randomly chosen young adult female is taller than 6 feet (about 182 cm)?”*
If we assume that female heights are normally distributed (a very close approximation is also okay),
we can find this probability by calculating a z score and consulting a z table (also called a normal
probability table). In Excel, this is done in one step with the function norm.dist (x, mean, standard
deviation, TRUE).
=1 – NORM.DIST(x, mean, sd, TRUE)
Note that this Excel built-in function gives the area under the normal curve to the left of a given
value, x, with a given mean and standard deviation (another way to say this: left tail cumulative
probability). Since we’re interested in the probability that someone is taller than 182 cm, we have
to take one minus that probability (we are finding the right tail cumulative probability). Refer to
page 133 in your textbook for why we do this.
Assuming a normal distribution has allowed us to calculate a theoretical probability. If we want to
calculate the probability empirically, we simply need to determine how many observations fall
above 182 then divide this number by the sample size. Tip: Use a counting rule to get Excel to
search the column of heights and count how many meet the criteria =COUNTIF(select
data,”>182″)/260, place the criteria inside of quotation marks. Although the probabilities are not
exactly the same, they are reasonably close. The closer that your distribution is to being normal,
the more accurate the theoretical probabilities will be.
Exercise, discuss this in the online discussion: Write out two probability questions that you would
like to answer; one regarding female heights and one regarding female weights. Calculate those
probabilities using both the theoretical normal distribution as well as the empirical distribution
(four probabilities in all). Which variable, height or weight, had a closer agreement between the
two methods?
Continue on to the next tab for more with this and the binomial distribution.
Probability Computation
Probability of randomly selecting a female whose height is greater than 182 cm
0.004259593 In Excel enter =1-NORM.DIST(182,164.9,6.5,TRUE)
Probabilities are usually rounded to 3 or 4 decimal places, but sometimes to 2 or more
than 4. Pay attention in assignments for rounding directions.
This week you also will be working with the binomial distribution and the normal
approximation to the binomial. Excel has built-in function for computing combinations
=COMBIN(n,k) and for computing binomial probabilities =
4
Here is an example from the slides, 4 chose 1 =COMBIN(4,1)
36
Here is an example from the slides, 9 chose 2 =COMBIN(9,2) There
are 36 ways to choose 2 items from 9 irrespective of order, that is
selecting items A and B is counted only once so selecting A and B in
either order is only counted as one possibility.
Here is an example from the slides, 2012 Gallop poll obesity rate is
used as p (26.2% is 0.262) and you are computing the probability of
8 (x) obese people in the sample of 10 (n) people:
=BINOM.DIST(8,10,0.262,FALSE) Tip: Format the cell to show the
0.000544171 value rounded to however many decimal places you need.
Interpretation: There is a probability of 0.0005 (or 0.5%) of
randomly selecting a sample of ten people (from the population
under study, Americans in 2012) and getting exactly 8 in the obese
range, as defined in this study.
Normal approximation to the binomial: For the Facebook example in your slides, use
=1-NORM.DIST(70,61.25,6.78,TRUE) to get the right tail probability, that is, to compute
the probability of greater than or equal to 70 friends. P(x>=70) Format this cell to show
4 decimal places if desired.
0.09835
Normal Approximation without continuity correction included =1NORM.DIST(70,61.25,SQRT(61.25*0.75),TRUE)
Histogram: Binomial n=245, p=0.25
0.0700
ccd6ddee64a660425769c01e046ddb52
0.0600
Probability Computation
Histogram: Binomial n=245, p=0.25
0.0700
0.08767
Binomial Computation using =1-BINOM.DIST(70,245,0.25,TRUE)
0.01068
The approximation is greater by 0.01068, with the rounded
standard deviation of 6.78 the example in the slides show a slightly
greater difference.
0.0600
0.0500
0.08616
Normal Approximation with continuity correction included =1NORM.DIST(70.5,61.25,SQRT(61.25*0.75),TRUE)
0.0300
0.08767
0.0200
0.0100
0.0000
0
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Binomial Computation using =1-BINOM.DIST(70,245,0.25,TRUE)
Using the continuity correction: The approximation is now less than
the binomial value by 0.00151, continuity correction is not discussed
in this text, but is common if you are looking in other sources and as
you see it improves the approximation process. However, in
-0.00151
practice, with software so prevalent you may never have a need for
the normal approximation process as shown here. For a brief
explanation of continuity correction go to the Normal
Approximation section in David Lane’s book.
Normal Approximation to the Binomial, David Lane and Rice University book
P(X)
0.0400
ccd6ddee64a660425769c01e046ddb52
Number of Successes
Lab 3: Exploring Normality
On Your Own
In the previous few guided Excel activities, you recreated some of the displays and preliminary analysis of the body
dimensions data. Your assignment involves further data analysis for this data set. You are to use the “save as” option to
save it as an Excel workbook in your statistics folder on your computer (or memory stick, cloud, etc.). Use this file or copy
the data and On Your Own sheets to a new Excel workbook and save it as your lab to submit.
1. Using the same technique herein for histograms and Q-Q normal plots, determine whether female weights appear to
come from a normal distribution. Do the same analysis for male weights. Create sheets for female weights and male
weights, get descriptive statistics and both charts from the provided web resource. Write a few sentences describing the
distribution (center, shape and spread of the data values).
2. Now let’s consider some of the other variables in the body dimensions data set. Using the figures on the next page,
match the histogram to its normal probability plot. All of the variables have been standardized (first subtract the mean,
then divide by the standard deviation), so the units won’t be of any help. If you are uncertain based on these figures,
generate the plots in Excel or https://www.wessa.net/rwasp_fitdistrnorm.wasp to check. Hint: Did you watch the video
on these plots, did you notice the sideways histograms next to the normal plots? The observed data is on the horizontal
axis of histograms, but on the vertical axis for the normal quantile plot (normal probability plot).
2.1) The histogram for female biiliac (pelvic) diameter (bii.di): normal probability plot letter __.
2.2) The histogram for female elbow diameter (elb.di): normal probability plot letter __.
2.3) The histogram for general age (age): normal probability plot letter __.
2.4) The histogram for female chest depth (che.de): normal probability plot letter __.
3. Note that normal probability plots C and D have a slight stepwise pattern. Why do you think this is the case?
4. As you can see, normal probability plots can be used both to assess normality and visualize skewness. Make a normal
probability plot for female knee diameter (kne.di). Based on this normal probability plot, is this variable left skewed,
symmetric, or right skewed? Use a histogram and descriptive statistics to confirm your findings. Answer using complete
sentences.
5. Using the sample statistics in the Excel NORM.DIST function, compute the following for the female population. State
the formula you entered in Excel, be sure this is shown on what you submit.
5.1) Probability of randomly selecting a female whose knee diameter is less than 18.1, P(x16.8) = ?
*
The study that published this data set is clear to point out that the sample was not random and therefore inference to a
general population is not suggested. We do so here only as an exercise.
This Excel lab accompanies OpenIntro Statistics, 3rd. edition and was adapted by Linda Currie to Excel 2016 from Lab 1
Introduction to Data for OpenIntro by Andrew Bray and Mine Çetinkaya-Rundel from a lab written by Mark Hansen of
UCLA Statistics.
46
Lab 3: Exploring Normality
Images for Number 2:
47
Lab 3: Exploring Normality
48