XVI 



Tables for Statisticians ami Biometricians 



[I 



the origin being the mean. Table I. gives the value of xjcr for each thousandth 

 of the area of this curve, — each ' permille ' — reckoned ffom left to right. 



In entering the table we enter from the left-hand column and top row if the 

 permille be less than 500. For example, if the frequency below a particular value 

 were 387 per thousand, the corresponding deviate would be — 0'2871, the number 

 placed at the intersection of the "SS row from left and 007 column from top. 

 The negative sign is always to be given when reading permilles below 500, 

 because the deviate will be in defect of the mean, supposing increasing variates 

 to be plotted as usual from left to right. 



On the other hand if the permille be greater than 500 we enter the table fiom 

 the right-hand column and bottom row. For example, if the permille be 748, the 

 deviate is -I- 0"6682, the number placed at the intersection of the •7-1 row from 

 right and ^008 column from bottom of the table. The plus sign must be given, as 

 the deviation is in excess of the mean, if the convention as to plotting variables 

 has been observed. 



Illustration: The following observations were made on the nature of the 

 degree taken by 1011 Cambridge undergraduates measured at the Anthropological 

 Society's Laboratory : 



Poll 



Third Class 



487 

 189 



Second Class 

 First Class 



182 

 153 



Find the deviates of these on a normal or Gaussian scale. 



The sums from the lowest to each class top are -187, 676, 858 and 1011 

 respectively. If we term with Francis Galton the one man in a thousand of 

 surpassing intelligence or special ability a " genius," we have on multiplying by 

 •0009891197 the reciprocal of 1011, the series for entering Table I. Thus we 

 lind: 



Hence 



Deviate.s : 



(•481) 

 (•482) 



A 

 Ax •T 



1 



•4817 



•6686 



•8487 



and -9990 



•0476 

 •0451 

 •0025 

 •00175 

 - ^0458 



(•668)^4344 



(•669)-4372 



A -0028 



Ax •e •ooies 



-^-•4361 



(•848)r0279 



(•849)r0322 



A ^0043 



A X -7 ^00301 



+ 1^0309 



(•999) 3^0902 

 -|-3^0902 



Supposing with Pearson* that 100 units of intelligence ("mentaces") separate 

 the lowest man of the First Class from the highest man of the Poll, we have 

 -I- 10309 — (— "0458) = 100/ cr, where o- is the standard deviation of intelligence. 

 Thus 0"= 100/r07G7 = 92^88 mentaces. Hence we conclude that the range of 

 Tiiird Class men is from - 4-25 (i.e. 9288 x (- •0458)) below to -|- 40^50 



* Biometiika, Vol. v. p. 109. 



