2 6 Records of the Indian Museum. [Voi,. XXIII, 



concerned. With 50 mm. without correction, /3, is = *03 32 04+^04 

 52 01. Thus ShepparcTs correction is not important. 





Values of &• 





1 rnm. 



3-50 46 + # 6o 17 





20 ,, 



3-45 16 21 ± 49 72 97 





30 ,, 



3-24 24 + -35 44 89 





50 ,, 



3-60 10 00 + 71 20 69 





00 ., 



3'45 36 + -48 5i 





50 „ 



3'54 75 34 ± '58 96 25 



(without correction). 



Though /? 2 does not seem to differ significantly from 3, there is 

 slight tendency towards lepto-kurtosis. 1 



The P.E. of /3. 2 for a Gaussian distribution is X\ ' ^24 and is 

 about ±'23 in our case. The magnitude of P.E. again shows the 

 want of significant divergence from meso-kurtosis. 



The effect of grouping is evidently quite negligible. The 

 above investigation has been most elaborate in character and is 

 sufficient to justify the application of <( grouped" statistical 

 methods to our present material. 



The foregoing analysis ma)' be summarized thus: — 



(1) With samples of 200, even such broad grouping as 100 mm. 

 does not introduce errors greater than the random error of sampling. 



(2) Up to 50 mm. the effect of grouping is absolutely negli- 

 gible. In the case of the Mean, the S.D. and the Coeff. of Varia- 

 tion, " grouping error ' is of the same order as ' ' random error ' ' in 

 samples of several thousands of individuals. 



(3) Sheppard' s correction leads to a very substantial improve- 

 ment in the S.D. and the even moments. The odd moments 

 (being near a critical value) are not affected very much. Speaking 

 generally, Sheppard' s correction should never be omitted. 



(4) The percentage variation in the higher moments is too 

 large to make it worth while calculating them directly. 



I speak with hesitation about another inference which may 

 perhaps be drawn from the above investigation. Small errors of 

 estimating stature — even up to perhaps a few mm. are not likely to 

 affect the Moan value very considerably (provided these errors are 

 random errors and not systematic). 



(> 



Full Corrections" of Pairman and Pearson. 



We shall now consider certain "full corrections" recently 

 discussed by Pairman and Pearson.* The object of the above 



' K. Pearson: "Skew variation, a Rejoinder" Biu/n. Vol. 4 (1906), p. 175 

 Also appendix 1 1. 



Eleanor Pairman and K. Pearson: "On Corrections for the Moment- 

 ( oefficienta <>t Limited Ranee Frequency Distributions when there are Finite or 

 Infinite Ordinates and am Slopes at the Terminals of the Range." Biom, Vol. 



: [-258. 



