8 Records of the Indian Museum. [Vol. XXIII, 



to Anthropologists, I have thought it advisable to include short 

 explanatory notes, which would have been unnecessary in a purely 

 Biometrical paper. 



I must also offer my apologies to the trained statistician. 

 Much of the work will no doubt appear to him to be quite superflu- 

 ous. I would remind him that one of our objects has been to 

 persuade the Anthropologists to adopt statistical methods. This 

 has necessitated detailed consideration of certain points which 

 ma} 7 appear obvious to a trained statistician. 



For example, a very full discussion of the effect of grouping 

 has been given. All frequency constants were calculated several 

 times over with very different units of grouping. It is then shown 

 that the effect of grouping is quite negligible within very wide 

 limits — a result which is of course quite familiar to all statisticians. 1 

 But as I found very wide-spread popular misapprehension regard- 

 ing this point I have considered it desirable to give an actual 

 empirical demonstration of the above fact. The discussion of 

 various " correction" for grouping will have its own interest to the 

 statistician. 



Another consideration has guided me in this introductory 

 paper. Any extension of a scientific method to new material 

 requires caution. Our Anglo-Indian data cannot be assumed to be 

 homogeneous in character, hence I have thought it desirable to 

 justify empirically the application of statistical methods to such 

 mixed data as the present material. The assumption of " nor- 

 mality " (i.e. of approximately Gaussian distribution) thoroughly 

 permeates many important statistical methods. It was therefore 

 necessary to investigate the question of frequency distribution in 

 great detail. 



The arithmetical labour has been very great specially as I 

 did not have any modern calculating machine to help me. This 

 want of mechanical accuracy ma} 7 have introduced some uncer- 

 tainty in the arithmetical results and this is why I have quoted 

 the arithmetic very fully in order to facilitate checking by others. 

 In the case of important "moments,' I have checked them 

 absolutely by working with different start points (i.e. different 

 base numbers). 



This is my first venture into the province of Biometry and 

 it is not unlikely that I have made mistakes. I have included 

 lull details of the statistical work in the hope that competent 

 liiometiicians will kindly help me by pointing out errors. I 

 nave retained six places of decimal in the arithmetic, not in the 

 vain hope of reaching an impossible degree of accuracy, but for 

 convenience of checking. It is difficult to attain agreement to the 

 second place in the final results unless about six figures are 

 retained in the intermediate calculations in this type of work. 



1 K. Pears >n, " Errors ol Judgment &c." Phil. Trans. Roy. Soc. Vol. 198A 

 jo;) "Associative Mating in Man." Biometrika Vol. 2, 1903, p. 485. The 

 authors note that "the system of grouping adopted is within wide limits im ma- 

 terial." 



