1922.] P. C. MahaIvAnobis : Analysis of Stature. 23 



P.B. Omitting 100 mm. the maximum difference is '0269, which 

 will be the P.B. in a random sample of 5,000 (with coeff. of varia- 

 tion equal to 4). Thus the effect of grouping is of the same order 

 as the effect of sampling in a group of 5,000. Hence we con- 

 clude that different units of grouping do not introduce any appre- 

 ciable errors in the Coefficient of Variation. 



From the Anthropological standpoint, the Mean, the S.D., 

 and the Coeff. of Variation are the most important constants. 

 For stature, with samples of 200 with Sheppard 9 s correction the 

 effect of even such a large unit of grouping as 50 times the unit of 

 measurement is in all these cases absolutely inappreciable. 



We shall however consider the other statistical constants 

 before concluding this portion of our work. 





Values of t> 2 . 







With Sheppard* s correction : — 





- 



1 mm. 



i*8i 62 61 



± 



•12 25 05 



20 „ 



1-83 04 98 



± 



•12 34 yy 



30 ,, 



1-83 94 72 



± 



•12 40 83 



50 „ 



1-82 10 42 



± 



.12 28 40 



100 „ 



1*67 Sy 



± 



•11 32 39 



+ 



•12 25 07 



+ 



•12 43 09 



+ 



12 6l 06 



+ 



•12 84 60 



+ 



•13 57 07 



100 mm. makes a difference of '1376, which is just about the 

 same as the P.B. Otherwise the maximum difference is '0232 

 which is only a sixth of the P.B. A random error of the same 

 amount will be produced in samples of 2800. 



Let us now compare the values obtained without Sheppard 9 s 



correction : r 



1 mm. i*8i 02 94 



20 „ 1-84 38 31 



30 „ i'86 94 72 



50 „ 1-90 43 75 



100 ,, 2*01 20 



100 mm. introduces an error of '1958 which is considerabh^ 

 greater than the P.B. 



The* effect of grouping has now become quite obvious, 20 mm., 

 30 mm. and 50 mm. now introduce steadily increasing error. 

 With 50 mm. the error has now amounted to '0881 which is only 

 frds of the P.B. 



We thus see that Sheppard* s correction is absolutely indis- 

 pensable here. With Sheppard' s correction the effect is quite 



negligible up to 50 mm. 



Values of p 3 . 



With Sheppard 's correction : — 



1 mm. = - '64 36 06 + -28 59 



20 ,, = — -30 87 16 + -29 27 



30 „ = - '46 86 97 + -29 86 



50 „ = - '47 7 8 44 ± '30 70 

 100 „ = - -48 35 78 ± -33 33 



