cxcvi Tables for Statisticians and Biometricians [XXXVIII XLI 



Hence rf" = 2'684,256. 



Again, 197*32/z 2 "' = 3025-4375 - 10*5325 + 37-2655,7780 



- 2-3180,3042 + 81-0846,7580 + 694 

 = 3824-9372,2318. 



Hence ^" = 19-384,438. 



Thus <r 2 = /ia'" - /u/" 2 = 19-384,438 - 7*205,230 = 12-179,208, 



and a- = 3*489,872 months, 



while the Mean= 1 + f*i" = 3-684,256 months. 

 Taking the month as 30*4375 days we have 



Mean = 112-14 days, 

 Standard Deviation = 106*22 days. 



Now suppose we make no abruptness corrections, nor use Sheppard's correction 

 in calculating the second moment, i.e. use merely raw moments, we find* 



Mean = 3'759,224 months = 114-42 days, 

 Standard Deviation = 3'41 7,31 4 months = 104*01 days. 



Using merely the Sheppard's correction, which is not legitimate, as the terminals 

 have no high contact, we have 



Mean = 114'42 days, and Standard Deviation = 103'64 days. 



Thus Sheppard's correction without the abruptness-coefficients changes the raw 

 second moment in the wrong direction. 



The reader must be warned that the obtaining of a possible value for q does not 

 necessarily prove that the frequency is asymptotic at x = 0. When the third and 

 fourth moments are worked out in this case, we find that the theoretical frequency 

 curve is not asymptotic. All we have really achieved is to find an asymptotic 

 curve which gives the first six subranges the same frequencies as the actual data. 

 But the corrected moments are much the same in a case of this type when we 

 apply the non-asymptotic formulae (vii) and (viii) with the use of (xiii) and (xiv). 

 This we will now proceed to do. 



We may determine first v\ and v* by continuous machining. Thus : 



Frequencies x a; 2 



63-99 x 0-5 x 0-25 



22-59 1-5 2-25 



18-58 2-5 6-25 



15-96 3-5 12-25 



13-30 4-5 20-25 



11-51 5-5 30-25 



10-61 6-5 42-25 



9-30 7-5 56-25 



8-74 8-5 72-25 



8-29 9'5 90-25 



7-51 10-5 110-25 



6-94 11-5 132-25 



Totals 197-32 741-770 5092-7900 



= 197-32iY =197'32v 2 ' 



* See below for / and v'. 



