xviii Tables for Statisticians and Biometricians [II — III 



= '67449 x standard deviation, we have the standard deviation of the difference 

 = 0"'04196. Hence the deviation in terms of the standard deviation 



= 0-21/(0-04196) = 5-0048. 



Table II, p. 8, gives the area |(1 + a) of the normal curve up to the abscissa x/a. 

 Noting the remark at the foot of the table, we have 



*/<t=5-00, ^(1 -fa) = -999,999,7133, 

 xja = 5-01 , \{1 + a) = "999,999,7278, 



A = 145, 



A x 48 70, 



x/a = 5-0048, | (1 + a) = -999,999,7203. 

 Hence } (1 - «)- -000,000,2797. 



Accordingly if we suppose the deviation as likely to be in defect as in 

 excess, the probability that we shall reach the observed deviation, or exceed it, is 

 2x|(l-«), and that we shall not is | (1 + a) — £ (1 — a), or the odds against the 

 result on a pure random sampling chance are -999,999,4406 to -000,000,5594, or 

 1,787,629 to 1, i.e. overwhelming odds. Thus we may reasonably argue that sons 

 in the professional classes in 1900 were substantially differentiated from their 

 fathers by a longer forearm of about £". 



Illustration (ii). Find the value in mentaces of the mean intelligence of Poll- 

 men, First, Second and Third Class men as given by the numbers in the Illustration 

 to Table I. 



The equation to the normal or Gaussian curve being 



N 



z = 



,-iW') 1 



V2tt<t 



we easily find that if there be * tabled ' ordinates z 1 and z 2 * at the abscissae 

 #! and x 2 , which cut off an area n 12 , then the mean x 12 of this area is given bj' 



x 12 = a-.(z 1 -z 2 )l(n 12 IN) (x). 



It will be sufficient to take the values of the abscissae already found, i.e. 

 ^/o- = - -0458, x 2 /<r = + -4361, 

 x 3 /<r = + 1 -0309, xja = + 3"0902. 

 We require the z's for these. For example : 



x = -04, z= -398,6233 



•05, z = -398,4439 



= -58, A, -1793 



A 2 - 397. 



* The symbol z here used is that of the Tables, i.e. —. — c -i (*/")'. 



