1922.] P. C. Mahalanobis : Analysis of Stature. 25 





Values of f 5 . 







With Sheppard's correction: — ' 







30 mm. 



-11-92 55 72 



+ 



5-87 n 



50 ,, 



- 7 7 s 2 3 



+ 



572 74 



100 „ 



-11-09 49 34 



± 



4 66 78 



Without Sheppard's 



correction : — 







50 mm. 



- 8*i8 04 94 



± 



640 46 



100 „ 



- 14-56 



± 



7'34 65 



The gross prob. error is again of the same order as f* b itself. 

 Hence there is very wide fluctuation in its value and Sheppard's 

 correction is not important. It should be noted however that 

 even now the maximum difference (inter se) is less than the P.B. 





Values of ^ fi . 



30 mm. 



121-83 05 ± 2993 43 



50 ,, 



15473 13 ± 29-03 98 



The percentage P.E. for normal curve is ^-^4-80 95 = 32 63% 

 With such large percentage variation it is quite idle to calculate the 

 higher moments directly. 



Pearson says in this connection 2 (( Constants based on high 

 moments will be practically idle. They may enable us to describe 

 closely an individual random sample, but no safe argument can be 

 drawn from this individual sample as to the general population at 

 large, at any rate so far as the argument is based on the constants 

 depending upon these high moments." 



Values of /?,. 



1 mm. -06 87 56 ± -07 97 81 



20 „ -oi 55 38 ± -oi 93 24 



30 „ -03 53 ± -03 57 68 



50 „ -03 78 10 + 06 55 55 



100 ,, -04 94 90 ± -06 31 



11. * 

 Remembering that f} v = -2- we are quite prepared for such 



wide fluctuations. It will be seen that /3, differs from zero by just 

 about the same amount as its own P.K. (calculated separately for 

 each) which of course implies that there is a tendency towards /?, 

 differing slightly form zero, but that with a small sample of 200 

 this tendency has not become quite significant. The unit of 

 grouping does not make any difference so far as this tendency is 



1 On account of the great Arithmetical labour, it has not been found possible 

 to calculate ^5 and jug with lower units of grouping. 



2 Draper's Company Research Memoirs: "On the General Theory of Skew 

 Correlation and Non-Linear Regression," p. 9. 



