xx Tables for Statisticians and Biometricians [II — III 



of 1 or 2 in the last place. This is, of course, amply sufficient for statistical 

 purposes, where four figures as a rule would be sufficient. 



Using formula (i) p. xiii we obtain : 



z 1 = -39852, z 2 = -23450, 



e, = -36275, e t - -00337. 

 Whence : 



»»i = + ~t -,v~ o- = - '8273o- = - 76-84 mentaces, 

 "4817 



•39852 - -36275 _„. 1I700 



x lt = H — ^ <r= + '192oo- = + 17'88 mentaces, 



■18o9 



•36275 - -23450 „,_, " . 



CCJ3 = H — — o-= + -7121a- = + 66-14 mentaces, 



'1801 



•23450 - -00337 , „„_ „„. 



x u = H o-= + l - o378o- = + 142-83 mentaces, 



"1503 



•00337 — 

 x 4x = + ™*T' o- = + 3-3700O- - + 31301 mentaces. 



Assuming as before the average man to have 300 mentaces of intelligence 

 we find : 



Average Poll-man has 223 mentaces. 

 Average Third Class man has 318 mentaces. 

 Average Second Class man has 366 mentaces. 

 Average First Class man has 443 mentaces. 

 Average man of "genius" has 613 mentaces. 



Thus the average First Class Honours man is twice as able as the average Poll- 

 man, and the average "genius" has not quite twice the ability of the average 

 Third Class Honours man. 



Illustration (iii). It is required to determine normal curve frequencies corre- 

 sponding to the following frequencies of the cephalic index in Bavarian skulls. 



Here the mean and standard deviation found by moments in the usual way are 



wi = 83-069, o- = 3-432. 



The deviations from the mean were next expressed in terms of the standard 

 deviation, i.e. these deviations are 



-13569, -12569, ... -0-569, + 431, +1-431, +2431, ... + 14431, 



and they are multiplied on a calculator by the reciprocal of the standard deviation, 

 whence the column xja is found. Table II gives us £(l+a) knowing xj a ; this 

 has been calculated by first differences only. We shall consider as an illustration 

 to Table XII, whether the normal distribution thus reached is to be considered 

 a good fit to the observations. 



