26 THE MEASUREMENT OP VARIATION. 



divides by the number of observations, and takes the 

 square root of the quotient. Thus: 



(or ff) = 



Where n = number of observations, and v = a devia- 

 tion from the average. For instance, to determine the 

 variability of the following series, representing the 

 frequencies of the numbers of veins in 26 leaves col- 

 lected from different parts of a beech tree,* we find the 



Number of veins, 15 16 17 18 19 20 

 Frequencies, 147941 



mean (IT. 5), determine the deviations from it in each 

 direction, and square them. Then the variability will 

 be represented by the square root of the following ex- 

 pression: 



(2.5)' X 1 + (1.5) a X 4+(.5) X 7 + (.5)' X 9 + (1.5)'X 4 +(2.5)*X 1 



i. e., by 1.15. 



This index of variability, or " Error of Mean Square," 

 is termed by Professor Pearson the " Standard Devia- 

 tion," or #, and its percentage ratio on the mean the 

 " Coefficient of Variation." It has been made use of 

 by Warren in the crab measurements already referred 

 to, and also in a very elaborate research f on the 

 variability of the skeleton of the Naquada race, a 

 people that existed in Egypt about 3500 B. c. It 

 has also been employed by Weldon, whilst Pearson al- 

 most invariably adopts it. Duncker $ has expressed his 



* Vide K. Pearson's " Grammar of Science," p. 382, 



fPhil. Trans. 1898, B. p. 135. 



\ Biol. Centralblatt, xvii. p. 785, 1897. 



