cxcviii Tables for Statisticians and Biometricians [XXXVIII XLI 



Illustration (ii). Obtain a curve to describe the data represented by the follow- 

 ing table*: 



The real r? 6 = 132. 



The data have clearly high contact at the tail, or all the K"s may be put zero. 

 We first turn to Table XXXVIII to find q at the assumed asymptotic start, and we 

 have from that table 



q= -7, ? e =- 253-6' 



q= -9, fl 6 = + 34-8 

 q =!(), ?? 6 = + 37 

 Hence by rough interpolation q = -9286. 



We might proceed to interpolate to find the K's but it is really adequate to 

 take q *9, whence Table XLI gives us 



#! = - 2604-306,99, K 2 = 1682-917,97, 



K 3 = - 1267 -010,60, #4 = 1119-669,46. 



Taking moments about a; = 1 as in Illustration (i), for all frequencies except 

 the first, we have 



(N-nJ vi" = 4027 *V" = 6107-5, (N- n^ v z '" = 4027^'" = 17,684-75, 



4027**,"' = 77,705-875, 

 By aid of equations (iv), we find 



4027^'" =451,458-6875. 



8192/tii'"= 3,503-193,01, or ^" = -427,636, 

 8192^"= 19,032-084,64, or rf" = 2-323,253, 

 8192 A< 3 /// = 74,911-989,40, or /* 3 '" = 9-144,530, 

 8192^ 4 '"= 443,853-436,13, or // 4 '" =54-181,328. 



These are the fully corrected moments of the whole system about x 1. Trans- 

 ferring to the mean we obtain 



Mean =1-427,636, 



^ 2 = 2-140,379, /* 3 = 6-320,416, ^ = 40-988,041, 

 and therefore fr = 4'073,98 and 2 = 8'946,97. 



* These data are really discrete, representing runs in experimental coin tossing, but the fitting of a 

 curve is a good illustration of the use of the asymptotic abruptness-coefficients. 



