1922.] P. C. Mahalanobis : Analysis of Stature. 75 



The stability of the Mean Value is remarkable. For the whole 

 series it was 3*57, for the selected races it is 3*571. It therefore 

 seems likely that 3*57 is very near the true typical coefficient of 

 variation [of stature) for homogeneous non-Indian samples. 



The S.D. is much reduced by selection. This is now '3590 

 as against '5450 for the whole series. We have selected the more 

 reliable values, but this has also excluded almost all extreme 

 values. Great divergence from the Mean value is thus probably 

 due more to paucity of material than to actual peculiarities of 

 distribution. 



Anglo-Indian V - 4*0672 



Selected Mean V = 3'57io 



Anglo-Indian Difference = -4962^-2421 



The actual difference is again the same, but this is now 

 nearly twice the Probable Error. 



We have, 



D 49*62 



x = — = — — = 1 -30 approximated 



°- 35*90 

 From Biometric Table II, J(i + *) = 9 1 62 04 7 



|(I -a) = -08 37 95 3 



Thus 8-38% of all reliable samples will actually be more 

 variable than Anglo-Indians, while 16*55% will differ more from 

 the Mean. 



Anglo-Indian Variability of stature is not significantly higher 

 than the average Variability of selected samples. 



(c) Selected and Weighted Series. 



Still another course is open to us. We can consider the 



1 weighted Mean " ] and " weighted" Standard Deviation of the 



Coefficient of Variation. For this purpose, we choose our weights 



to be proportional to i/E* y where E is the probable error, i. e. 



give " weights " proportional to reliability. 



We get, 



Weighted Mean 7 = 37622 



Weighted S.D. of Mean V = -1846 



We notice that the Mean is now considerably higher. This is 

 due to the much greater reliability in the measurements of the 

 more civilised races, who have invariably higher variabilities. This 

 greater value is also due in a large measure to the weight of the 

 U.S.A. recruits (^ = 7623 against 10 for the lowest weight) which 

 includes 25,898 individuals. 



1 See Yule: " Theory of Statistics " (Charles Griffin. 1919), p. 220. 



