+ 



•28 93 



+ 



•29 14 



+ 



•28 yi 



+ 



•25 39 



24 Records of the Indian Museum. [Voi,. XXIII, 



100 mm. is not at all worse than others. The maximum error 

 (which now occurs in the 20 mm. group) '3349 just exceeds the 

 P.E. 



Without Sheppard" s correction : — 



20 mm. = -30 8j 



30 „ = .46 55 



50 „ = .47 j8 



100 ,, = -66 40 



Evidently Sheppard 's correction does not produce substan- 

 tial improvements. In this case the gross P.E. of /i 3 is of the 

 same order as M3 itself and hence there is wide fluctuation in the 

 result. 



In view of the large P.E. we cannot say that grouping makes 

 any significant difference. The asymmetry is very slight and very 

 nearly zero, thus the fluctuations though large are not statistically 

 significant. These wide fluctuations indicate the critical approach 

 to the Gaussian curve. 



Values of /* 4 . 



With Sheppard's correction : — 



1 mm. 11*56 10 21 ± i*54 15 



20 ,, 11-56 54 26 + 1-56 59 



30 „ 10-97 ri 78 ± 1*58 08 



50 „ 11-94 16 22 + 1-54 97 



J oo „ 10-35 96 ± 1-31 58 



100 mm. makes a difference of 1*2014 which nearly equals the 

 P.E. Otherwise the agreement is good. The maximum error is 

 •59 (in the 30 mm. group) which is much less than -J the P.E. 

 Random error of the same amount will require samples of 1300 

 individuals. 



Without Sheppard's correction the agreement is much worse. 

 We have 



1 mm. 11*56 10 21 + 1-54 15 



20 ,, 1170 20 ± 1-58 8y 



30 „ 11-30 37 ± 1-63 31 



50 ,, 12-86 56 42 ± 1*69 46 



100 ,, 13-98 12 48 ± 1-89 13 



100 mm. has become loo " rough ' ' and 50 mm. itself introduces 

 an error of about the same order as the P.E. Thus Sheppard's 

 corrections make substantial improvement in the results. The 

 percentage probable error of /u 4 for normal curves is given by 



Jxi'V 96= 15-7% in our ease. In view of this large percentage varia- 

 tion, observed agreement with different groupings is quite satis- 

 f actor v. 



