Ill] THE COEFFICIENT OF VARIABILITY 125 



which is independent of any particular units, and which is called 

 the coefficient of variability''^ . 



Karl Pearson, measuring the amount of variability in the weight 

 and height of man, found this coefficient to run as follows : In male 

 new-born infants, for weight 15-6, and for stature 6-5; in male 

 adults, for weight 10-8, and for stature 3-6. Here the amount of 

 variability is thrice as great for weight as for stature among grown 

 men, and about 2 J times as great in infancy f. The same curious 

 fact is well brought out in some careful measurements of shell-fish, 

 as follows; 



Variability of youdg Clams (Mactra sp.)X 



The phenomenon is purely mathematical. Weight varies as the product of 

 length, height and depth, or (as we have so often seen) as the cube of any one 

 of these dimensions in the case of similar figures. It is then a mathematical, 

 rather than a biological fact that, for small deviations, the variability of the 

 whole tends to be equal to the sum of that of the three constituent dimensions. 

 For if weight, w, varies as height x, breadth y, and depth z, we may write 



w = c.xyz. 



„„ ,.„ ,. ,. dw dx dy dz 



Whence, ditterentiatmg, = h -^ H . 



w X y z 



We see that among the shell-fish there is much more variability 

 in the younger than in the older brood. This may be due to 



* It is usually multiplied by 100, to make it of a handier amount; and we may 

 then define this coefficient, C, AS — ajM x 100. 



t Cf. Fr. Boas, Growth of Toronto children,- Rep. of U.S. Cornm. of Education, 

 1896-7, 1898, pp. 1541-1599; Boas and Clark Wissler, Statist cs of growth, 

 Education Rep. 1904, 1906, pp. 25-132; H. P. Bowditch Rep. Mass. State Board 

 of Health, 1877; K. Pearson, On the magnitude of certain coefficients of correlation 

 in man, Proc. R.S. lxvi, 1900; S. Nagai, Korperkonstitution der Japaner, from 

 Brugsch-Levy, Biologie d. Person, ii, p. 445, 1928; R. M. Fleming, A study of 

 growth and development. Medical Research Council, Special Report, No. 190, 1933. 



J From F. W. Weymouth, California Fish Bulletin, No. 7, 1923. 



