SOCIETY OF THE UNIVERSITY OF ABERDEEN. 



97 



positive in two quadrants and negative in the other two quadrants, 

 as indicated in the figure. In getting the total we of course subtract 

 the negative products from the positive products. 



For the 364 Aberdeenshire peasantry I have found 



2(zy) = 4933. 



We obtain (/) about the means by the formula 



where -7 and y are the distances of the arbitrary axes from the mean 

 axes. 



This gives %(xy) = 4933 - 364 x xy. 

 = 4933 - 772-53. 

 = 4160-47. 



4160-47 



" 364 x 5-64 x 4-88' 

 = -41454. 



Seeing that the maximum possible correlation is unity, this in- 

 dicates a fairly high correlation between breadths and lengths of head, 

 or, strictly speaking, between their deviations from the means, among 

 the East Aberdeenshire peasantry. 



PROBABLE ERROR. 



Every value calculated from the statistics of a sample is liable 

 to be different when calculated from another sample of the same 



M P 



population. The frequencies of deviations from the mean value follow 

 the normal curve just as they do in tossing pennies or throwing dice. 

 A deviation MP, which makes the two cross-hatched areas equal, is 



13 



