Butter-Fat Percentage in Jersey Cattle. 139 



percentage. Reflection on the purpose of the coefficient of vari- 

 ation will make clear that the use of coefficients of variation 

 comes in ridding the coefficient of the terms in which the data 

 .are recorded. In other words the coefficient is made a pure 

 number. This is also just what an index does, consequently the 

 use of a coefficient of variation of an index is somewhat like cal- 

 culating the variation of a pure number. How much this in- 

 fluences the conclusions to be derived from such coefficients of 

 variation is a matter of some doubt. That there is some influ- 

 ence is known; it is, however, altogether probable that this dis- 

 turbance is not so great but what some conclusion may be drawn 

 from the calculated coefficients of variation even admitting these 

 disturbances. 



The need for such a comparison become especially clear in 

 our data on butter-fat percentage. Here the character studied 

 is the concentration of the butter-fat in the milk and not the 

 total mass or pounds of this fat secreted for a lactation. Infor- 

 mation is desired on the variation of the functioning of the cells 

 which secrete this concentrated fat emulsion in comparison with 

 those of cells of the mammary secreting a low concentration of 

 fat. Furthermore comparison data for the variation of the 

 ability of other glandular cells in their secretory activity is de- 

 sirable. For these reasons it has seemed best to present coeffi- 

 cients of variation for such data realizing in so doing that too 

 wide conclusions cannot be drawn from them. The data for this 

 comparison are given in Table 2. In this table are also includ- 

 ed, to save the table space, the calculated skewness of the fre- 

 quency distributions as these data will be used shortly. 



The standard deviations of the butter-fat percentage of the 

 milk produced by the four breeds, Jersey, Guernsey, Holstein- 

 Friesian and Ayrshire shows a relation to the mean concentra- 

 tion of this butter-fat, such that, the breeds producing the great- 

 est concentration have a significantly larger variation than do 

 the breeds whose milk contains less fat. The solids other than 

 the butter-fat, contained in the milk of the Holstein-Friesian 

 cows, show approximately the same standard deviation as does 

 the butter-fat of this breed. Such mean solids-not-fat percent- 

 age of about two and one-half times the mean butter-fat per- 

 centage leads to a coefficient of variation of about half the size 

 of that for the butter-fat percentage. 



