160 ADOLF H. SCHULTZ 



the squares of the deviations of the individual values from the 

 average of the row and expresses the absolute variability: 



(T = W-S(F — M)-. The variation coefficient (v) expresses the 



standard deviation in percentage of the average, whereby a 



criterion for the relative variability is obtained : v = -—-- . The 



correlation coefficient (r) affords a means of determining the law, 



according to which two characteristics combine. It is the sum 



of the products of the deviations of the two characteristics from 



the corresponding averages taken for each individual, divided by 



the product of the number of individuals and the two standard 



2 (x — X) (y — Y) 



deviations : r = — — ~ . A complete correlation 



na^ ay 



exists when r = 1. If r = 0, no relation prevails between the 

 two characteristics. A positive correlation coefficient indicates 

 a change of the characteristics in the same direction, a negative 

 one, in the opposite direction. Finally, to test the degree of 

 exactness of the above formulae, the probable error (E) was de- 

 termined by the following formulae: 



EiM) = ± 0.6745 -J- for the average. 



■\ n 



E {a) = ±0.674:5—; — •- for the ptaudard deviation. 



V2ft 



V 



E (v) = ±0.6745— — for the variation coefficient. 



V2//. 



If r > 10, the hist forinuhi must be multiplied bv -v'l + 2 ( — - ) 



- \ VlOO/ 



E (r) = ±0.6745 — r^— for the correlation coefficient 



■\ n 



The relation of the insertion of the muscles to the length of the 

 humerus makes a short prehminary discussion of this absolute 

 measurement necessary. Table 1 is a compilation of the aver- 

 ages and the conditions of variability of the length of the two 

 hiuidred and ten humeri, which were measured. The extremes 

 of these measurements range from 260 to 367 mm. The humerus 

 in male whites is on the average 26 mm., in male negroes 31.8 mm. 



