Sept. 15, 1919 Variation in Milk of Ayrshire Cows 301 



direction of heightened variability and also in certain other respects which 

 need not be gone into here. 



5. Comparison of the present results with those of Gavin (2, 3) leads 

 to the same conclusions as those reached in the preceding paragraphs. 

 In Gavin's first paper (2), where 1,233 normal lactations of cows of all 

 ages lumped together are discussed, coefficients of variation are given as 

 follows: For total lactation yield 25.72; for average daily yield 25.78; 

 for maximum daily yield 24.68; and for revised maximum daily yield 

 24.77. These values are of the same order as those from Vigor's data 

 (coefficient of variation about 24.2) and from the total combined dis- 

 tributions (Table V) of the present paper. In a later paper Gavin (j) 

 deals with each of the first five lactation periods separately for a group 

 of about 375 cows. From his data we find the weighted mean coefficient 

 of variation for these five lactations to be 17,998, a value sufficiently 

 close to our weighted mean value for single years of age. 



6. Turning to the fat percentage, we see that Vigor's values of 3.681 

 for the mean and 0.323 for the standard deviation are substantially 

 identical with our weighted mean values of 3.738 and 0.330. Pearson 

 (2j) has also given some reductions for variation in Ayrshire fat per- 

 centages, and the present values are again in close accord with his. 



7. It may be concluded that the values of the means and variabilities 

 here given represent essentially normal values for Ayrshire cattle. 

 These constants will be of considerable usefulness as time goes on, for 

 purposes of comparison with other breeds and in the study of special 

 problems. 



THE COMPARATIVE VARIABILITY OF MILK PRODUCTION 



Milk production is essentially a physiological character. It is a matter 

 of some interest and significance to examine the variability of the 

 character in comparison with other physiological characters and also 

 with some that are more strictly morphological, as, for example, bone 

 measurements. Such comparisons may be made through the coefficients 

 of variation. It must, however, always be kept clearly in mind just w^hat 

 a coefficient of variation is ; and care must be taken to avoid drawing too 

 sweeping or even entirely unjustified conclusions from comparison of 

 these constants. What the coefficient of variation measures is the per- 

 centage which the "scatter", or variation exhibited by a distribution as 

 measured by the standard deviation, is of the mean of the character vary- 

 ing. For some purposes this percentage is meaningless. It is therefore 

 idle to try to force its use for those purposes. It will undoubtedly be 

 presently supplemented by some other constant for the measurement of 

 other aspects of comparative variability. It has, however, a perfectly 

 definite, if limited, meaning. It is a unique constant of any distribution, 

 expressed in abstract units. As such it may be used for purposes of 

 comparison, always remembering that one must be cautious as to the 

 maimer in wliich conclusions drawn from such comparison are stated. 



