Variation in Hooks of Dog-Tapeworms 21 



Part II. Mathematical 



BY C. C. ENGBERG 



This paper is devoted chiefly to the study of the variability of 

 the various parts of the hooks of the dog-tapeworms, Taenia 

 serrata and T. scrialls, and the correlations of these parts to one 

 another. The data used are those obtained by Mr. E. C. Steven- 

 son, who discusses them from a zoological standpoint in Part I 

 of this joint paper. In these discussions certain mathematical 

 constants and formulae are used, which may be denned here. 



1. The Standard Deviation, abbreviated S. D. and symbolized 

 by the Greek letter a. It may be proved both mathematically 

 and physically that the measure of variability is that deviation 

 from the mean magnitude whose square is the mean of the squares 

 of the individual deviations. The mathematical statement of 

 this is 



a = \ 



-ZxKf 



< 



Sum of [(deviation of class from mean)' 2 , frequency of class] 

 number of variates. 



2. The standard deviation gives the absolute variability of the 

 character under consideration, while for purposes of comparison 

 a relative measure is required, as is seen from the fact that the 

 difference of a ton in the weight of two elephants is not rela- 

 tively so large as a difference of an ounce in the weight of two 

 mice. A good relative measure of the variability is obtained by 

 dividing the standard deviation by the mean (M) and multi- 

 plying by 100, which gives the coefficient in terms of per cent; 

 that is, the coefficient of variability. 



F= F .ioo% 



211 



