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



Standard Deviation. 



Let us first consider the results without Sheppard' s correction. 



i mm. 67-385 + 2*557 mm. 



20 „ 67-894 + 2-547 „ 



30 „ 68-365 + 2-444 >i 



50 „ 69-00 ± 2-679 „ 



100 ,, 70-922 ± 2-662 ,, 



With 100 mm. the difference is quite large. It is 3*537 mm. 

 which is considerably greater than the prob. error. Omitting 100 

 mm. we find the maximum difference to be i'6i5 mm., which is 

 considerable, but is still less than the P.E. Such a P.E. will be 

 obtained with samples of 400. Thus the agreement without Shep- 

 pard' s correction is not very good. 

 With Sheppard' s correction 



1 mm. 67-385 + 2557 mm- 



20 ,, 67-648 + 2-539 >> 



30 „ 67-812 ± 2-426 „ 



50 „ 67-473 ± 2-619 „ 



too „ 6477 ± 2-432 „ 



100 mm. is again discrepant. The difference is 2*615 mm. 

 which is of just the same order as the P.E. Evidently 100 mm. 

 grouping is too broad and the error due to grouping is no longer 

 negligible. This is also obvious from the fact that Sheppard 's 

 correction makes the S.D. actually less than its true value, while 

 the uncorrected value is considerably greater. 



Omitting 100 mm. the agreement is excellent. The maxi- 

 mum difference (which is now in the 30 mm. group) is only "427 

 mm., a value about a sixth of the probable error. It will require 

 a sample of 6000 to produce a random error of the same amount. 



Thus with Sheppard's correction, the effect of grouping is 

 quite negligible up to 50 mm. These corrections are so easily 

 applied that there can be no excuse for omitting them. We have 

 thus empirically verified the great importance of Sheppard's 

 correction in giving better values of the Frequency Constants. 

 Henceforth it will not be necessary to compare the values obtained 

 without Sheppard's correction. 



Coefficient of variation : V — — — - 



1 mm. 4*06 72 + -13 74 



20 „ 4-08 29 ± -13 79 



30 „ 4-09 41 ± -13 83 



50 „ 4-07 38 ± #I 3 76 



100 „ 3-90 29 ± '13 18 



100 mm. is obviously incorrect, we may omit this group from 

 further consideration. The difference '1643 is greater than the 



