xviii Tables for St<it!xii<-i<ni* <m<l />i/i/< trlcians [II III 



= -(J7449 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 + o) of the normal curve up to the abscissa xja. 

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



xfa- = 5-00, i (1+ a) = "999,999,7 1 33, 

 x\a = 5-01 , J (1 + a) = -999,999,7278, 



A = 145, 



A x 48 70, 



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

 Hence J (1 - a) = -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 

 2 x ^ (1 a), and that we shall not is J (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 



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

 Xi and x t , which cut off an area n n , then the mean Xj 3 of this area is given by 



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

 XI/<T = - -0458, XI/<T= + -4361, 

 x t /a = + I -0309, x t l<r = + 3-0902. 

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



x = -04, z = -398,6233 



05, z = -398,4439 



= -58, A, -1793 



A., - 397. 



* The nymbol t here used is that of the Tables, i.e. -^ -*</)'. 



V2r 



