1922.] 



P. C. MahaIvAnobis : Analysis of Stature. 



49 



We finalty get the following for the shorter end of the frequency 

 distribution 



N 



= 112 



Mean = 1635- 14 mm. 

 S.D. = 70*23 mm. 



This gives a f£ shorter" group differing in the average stature 

 but with about the same variability as the total sample. 



Let. us now turn to the taller end. 

 Curtailing at 1705, we get 



Group 



1705 

 -1725 



-1745 



IO'O 



-1765 



-1785 



-1805 



-1825 

 O 



-1845 



-1865 



Total. 



Frequency . . 



18-5 



5'o 



IO'O 



2-0 



I'O 



I'O 



47'5 



With origin at 1705, raw moments are 



v,'=2*00 



v 2=6'73 4 2 IX > leading to ^ = 273 42 n 

 y, =068 33 

 Thus h' =070 71 

 if/ 2 =i*68 18 

 and we obtain 



N = 198 x 



Mean = 1659-02 mm. 

 S.D. = 67-27 mm. 

 which is practicahy identical with the whole sample. 



Thus the " taller " end seems to represent a homogeneous sample 

 of the whole group , and starting from the taller end, we do not succeed 

 in breaking up the given frequency distribution into two normal sub- 

 groups. 



The tc shorter "end gives a pseudo-component. I shall show 

 later on, when we consider the question of age-differentiation that 

 the shorter tail represents approximately the smaller age groups. 



Asymmetrical Dissection. 



We have seen that our frequency curve is slightly asymmetric. 

 As Pearson observes, 1 ""the asymmetry may arise from the fact 

 that the units grouped together in the measured material are not 

 really homogeneous. It may happen that we have a mixture of 

 2, 3, .... n homogeneous groups, each of which deviates about its 

 mean symmetrically and in a manner represented by the normal 

 curve." 



Karl Pearson: "Contributions to the Mathematical Theory of Evolution 

 I. On the Dissection of Asymmetrical Frequency Curves," Phil. Trans. Roy. 

 Soc, Vol. 185A, 1894, p. 72. 



