xviii Tables for Statisticians and Bionietricians [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/<r. 

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



a:/o- = o-00, ^(1 + a) = -999,999,7133, 

 x/a = 5-01 , i (1 + a) = -999,999,7278, 



A = 145, 



A X 48 70, 



ajja- = 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 

 2 X 1(1 — a), and that we shall not is i (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 4". 



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 



v27ro- 



we easily find that if there be 'tabled' ordinates z^ and Z2* at the abscissae 

 a\ and x„, which cut off an area iii.,, then the mean Xjo of this area is given bj' 



J;, = a.{z,-z.M>H,/IP, (X). 



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

 ay<7 = - -04.58, .r,/o-=+ -4361, 

 x,/ar = + 10309, a-Vo- = + 3-0902. 

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



a; = -04, ^ = -398,6233 



•05, z = -398,4439 



^ = •58, A, -1793 



A, -397. 



• The symbol z here used is that of the Tables, i.e. ~ — c~* '*'"''. 



\ '2t 



