xxviii Tables for Statisticians and Biometricians [DL — XI 



But our value of S a /^ 2 is '5517. Thus we find by interpolation 



«'=-10G0. 

 It remains to determine m , «ij and m 2 for this value of x, or simpler £ + m , 



\ + m 2 and — m, from the above values for x = "1 and x' = "2. We find 



V27T 



\ + m, = -542,194, £ + m, = -500,184, --L - m, = -396,598. 



V27T 



Whence d/a = |||^ + '1060 = '8375. 



Thus <r = 5-5786/(-8375) = 6-6610 sees., 



x = x x a = '7061 sees., 

 njN = -5422. 



This gives a mean of 28'29 sees, with a variability measured by 666 sees. 

 Those actually registered as trotters are 54 °/ of the population. 



Table X (p. 24) 

 See under Table IX, p. xxv. 



Table XI (p. 25) 



Constants of Normal Curve from Moments of Tail about Stump. (Pearson and 

 Lee, Biometrika, Vol. vi. pp. 65 and 68.) 



This Table may be of service in cases of the following kind : 



(a) In some cases a record is actually truncated as in the case of the 

 American Trotters dealt with on p. xxvi. Or, again, we may take a record of 

 stature obtained by measuring all men who exceed 69", or a record of mental 

 capacity found by measuring all persons with low intelligence in a community. 



(b) When we recognise heterogeneity, e.g. when we have a mixture of male 

 and female bones, or two strains of trypanosomes, we can occasionally get a rough 

 approximate analysis by supposing the tails to represent homogeneous material 

 and then fitting them with normal curves. From the tails we get two components, 

 and if their compound agrees fairly well with the observed total we have 

 performed an analysis far more rapidly than by using the nonic equation*. 

 Difficulties arise owing to deviations from Gaussian frequency being not infrequent; 

 different dichotomic lines may give different results, and owing to paucity of 

 material in the 'tails' and corresponding irregularity there will be large probable 

 errors. 



Cases under (a) and (b) will be treated by exactly the same process, but our 

 Table supposes that the distribution considered is less than half the normal distribu- 

 tion. The rules for determining the mean, standard deviation and total frequency 

 of the untruncated population are given on p. 25 under Table XI itself. 



* Pearson, Phil. Trans. Vol. 185, A, p. 84. 



