1922.] P. C. Mahal anobis : Analysis of Stature. 



73 



(a) Whole Series. 

 Distribution of 100 Coefficients of Variation of Stature. 



Group 



Frequency 



1 80 



2'20 



2*6o 



3-00 



3-40 



3-80 



4-20 



to 



to 



to 



to 



to 



to 



to 



2'20 



2'6o 



3-00 



3-40 



3-80 



4'20 



4-60 



2 



1 



3 



9 



20-5 



34*o 



20-5 



8-o 



Beyond Total. 



4-60 



100 



Grouping in units of 4^ we find moment-coefficients about 

 the Mean, 



^ 2 = i-88 66 



^3= ~'77 8o 



^=ir6i 74 74 

 giving /?, = -09 46 73 



A* = 3-37 26 20 ±-63 30 

 with sk. = " -13 44 8 



Mean Coefficient of Variation =3 57 00 

 and S.D. of Coefficient of Variation = "545° 



Curve belongs to Type IV, but the Gaussian itself will be 

 quite adequate. 



( ' : Goodness of Fit" of Coefficients of Variation. 



Coeff. of V. 



Observed 



m' . . 



Theoretical 



m. 



m — m'. 



(m—m') 2 

 m 



Beyond 2*20 



2 



742 



1-258 



2-1320 



2-20 — 2-60 



3 



3-538 



•538 



•0818 



2-60—3-00 



9 



11-512 



2-512 



•548i 



3-00—3-40 



20-5 



22-912 



2*412 



•2531 



3-40-3-80 



34 -o 



27'934 



6-066 



1-3170 



3-80—4-20 



20-5 



20*769 



•239 



•0028 



420— 4-60 



80 



9'459 



i'459 



•2250 



Beyond 4-60 



3-0 



3*130 



•130 



•0054 



A — 



n' = 8 



4-5660 



#' 2 = 4-566 



P= 71 21 63 



Thus the Gaussian gives excellent fit. In seven cases out of 

 ten, the fit will be worse. 



We notice that one terminal frequency gives rather a large 

 value i.e. 2*1320, combining the two end groups, we get, 



X 2 = 2-555 



n' = 8, P= -85 45 87 



The fit is now considerably improved. / conclude that the 

 Coefficient of Variation {for homogenous groups) can itself be gra- 



