\ \ \ VIII XLI] 



Introduction 



K! = - 604-161,373, 

 K z = + 559-648,063, 

 K s = -535-911,377, 

 #4 = +523-571,319, 



Here the combined frequency on every pair of half-unit ranges, other than the 

 first and last, is identical with that of the original data, and the first and last sub- 

 ranges have also the frequencies of the data. 



To this table of revised data we can apply directly the method of the present 

 section. The q's at the two terminals will of course be the same, i.e. "12 and '44, 

 but it will be quite adequate to take them '1 and "4. We have 



ni' = 676-0/1715, n,' = 861/1715, ... n 5 ' = 407/1715, 

 n' p = 320-0/1715, n'p_i = 801/1715, ... n'p_4 = 35-5/1715, 

 whence we deduce from Table XLI 



Jfi' = + 242-593,046, 

 AY = - 195-592,259, 

 K 3 ' = + 171-309,304, 

 #4' = -159-045,916. 

 We now take as before the moments of N n 1 n p = 7l9 about x = 1 and find 

 in the working units 



/" = 6214-1, 719i> 2 "' = 80,492-95, 



'" = 1,174,477-325, 719*/ 4 '" = 18,049,426-3375. 

 Further p 2 = 18, whence by formulae (vi) 



rf" = 6-771,155, // a "' = 112-659,148, 



nj" = 1903-228,954, ^" = 33,173-876,879, 

 are the moment coefficients about x=l. 



Transferring to the mean x = 1 +MI'" = 7-771,155 we have 



^2 = 66-810,601, /* 3 = 235-626,406, /x 4 = 6310-921,674, 

 yielding fr = 186,171, & = 1-413,846, 



corresponding to a U-curve of Pearson Type I. 



In order to make the curve fit the range at 20, we must neglect ft t , and fit 

 only by the range, (6 = 20), fa, /* 2 and the mean. 



