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 : 



^, = -39852, ^3= -23450, 

 2„ = -36275, ^, = -00337. 



Whence : 



— -'?OSt'> 

 x^.^= + - ,01; q-=- -82730- = - 76-84 mentaces, 

 ■4817 



-39852 - -36275 ,_.. ,1-700 



0^2 = H Y^^T^ <r= + ■192o(7 = + 17-88 mentaces, 



-362 75 - -23 450 

 •1801 



«23 = + rTTTTTT- o- = + -71210- = + 66-14 mentaces. 



•234.50 - -00337 , -, -o-ro .t^too 



a-j. = H r-^r^ 0-= + l-o378a- = + 142-83 mentaces, 



" -1503 



Xi^ = + -^ qq' o- = + 3-37OO0- = + 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 



m = 83-069, a = 3432. 



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

 deviation, i.e. these deviations are 



-13-569, -12-569, ...-0569, -I- 431, -t- 1-431, 4-2-431, ... -H 14-431, 



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

 whence the column x/a- is found. Table II gives us ^(l+a) knowing .r/o- ; 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 t(j the observations. 



