708 APPENDIX 



The value obtained for r on page 705 is 



where x and y represent deviations from the means, and the summation is 

 extended to every pair of corresponding deviations. The calculation of 



^xy 



- can be much shortened by an equivalent formula which we shall 

 *fi<r 



now derive. Let G x and G y represent class marks near the means of the 

 systems of variates indicated by the subscripts, and C x , C y corrections to 

 these class marks which give the correct mean values so that 



Af x = G x + C x , 



My = G y + Cy . 



Let x'^y' represent deviations from G x and G y which correspond to 

 deviations x, y from the mean. Then 



C x ) - C x ^(y + Q 



n 

 This is a formula much better adapted to computation than the formula 



n<r x <r y 



Its application is shown in the text, page 465. 



SECTION IX RANDOM SAMPLES 



We know full well that we cannot, in general, measure all the individ- 

 uals of a race or population whose characteristics we wish to describe. We 

 are obliged to get our information and to construct our science by the 

 selection and examination of samples taken at random from a large group 

 of individuals. To illustrate, it is not practicable to measure the stature, 

 nor, in general, any other character of all the adults in the United States. 

 We must be content to deal with a reasonably small number that will make 

 the measurements a feasible undertaking. 



An investigator is always concerned about the number of variates which 

 must be measured in order that confidence may be placed in his results. 



