BIOMETRY 65 



square root of the final quotient. To distinguish it from the 

 average deviation, this is called the standard deviation. Its 



It forms a measure of the degree of 



formula is cr = 



\ n 



scatter of the variates. This measure is expressed in the same 

 units as were employed in measuring the variates. 



3. To compare one case of variation with another as re- 

 gards degree of scatter of the variates, another expression has 

 been devised which is called the Coefficient of Variation. It 

 is obtained by dividing the standard deviation by the mean. 



Formula, C F = — ^ It is an abstract number expressing 



the variability in per cent of the mean. 



Judged by their coefiicients of variability. Harvard stu- 

 dents are found to be more variable in weight than in height, 

 the respective coefficients (C V) for height and weight being 

 3.76 and 11.94. See Tablet. 



4. Another important tool of the biometrician should be 

 mentioned, viz., the coefficient of correlation, which is a 

 measure of the extent to which one character varies in 

 agreement with another. 



In order to obtain a coefficient of correlation a set of 

 observations may be classified simultaneously as regards 

 two characteristics. Thus we might inquire is there any 

 correlation between the height and the weight of men, and if 

 so how much ? Are tall men on the whole heavier than short 

 ones or vice versa ? To determine this matter we must first 

 obtain observations on the height and weight of the same 

 individuals. The observations may then be classified in a 

 correlation table (as in Table 1), which is made by ruling 

 paper into squares and entering the observations on height 

 in vertical columns, and the observations on weight in hori- 

 zontal rows, or vice versa. An individual 156 cm. in height 

 and weighing 48 kilos will be entered in the square at which 

 column 156 and row 48 intersect; an individual of the same 

 height but ten kilos heavier will be recorded in the third 

 square below, and so on. When all the observations have 



