138 Maine Agricultural Experiment Station. 1920. 



twenty-eight herds as to the amount of butter-fat produced in 

 its milk. The variation of this average butter-fat is between 3.05 

 and 5.12 per cent and the Jerseys are more than two per cent 

 greater in mean butter-fat percentage than are the lowest cows 

 of the species. It is especially instructive to study the distribu- 

 tion of these tests a little more closely. For this purpose the 

 tests were grouped into two-tenths per cent intervals. Such a 

 distribution gives some appreciation of the hereditary factors 

 which may be expected to occur in the given breed. The results 

 of such a grouping show that there are two breeds the Jersey 

 and the Guernsey at the top of the scale for the butter- fat con- 

 centration of their milk. The percentage is around 5 per cent. 

 In the other group are included the breeds of cattle with a mean 

 butter-fat percentage around 2>-7- Between these two groups 

 there is a distinct break between a mean percentage of 4.2 and 

 4.6. Such a break is highly suggestive of an hereditary differ- 

 ence of at least one unit between these breeds. In this connec- 

 tion the range or spread of the frequency distributions taken for 

 ^ach of these high and low test groups is of interest. Taking 

 the data from the Jerseys of this paper and the Holstein-Friesian 

 of the above mentioned paper the range of butter-fat for the 

 first is 3.65 to 6.95 while that for the Holstein-Friesian is 2.4 

 to 4.8. As the two frequencies are not very far from normal 

 and as what skewness there is is plus, it follows that the over- 

 lap of these curves constitutes only a small area of the total 

 covered by them. The differences of the two breeds are there- 

 fore quite distinct. The differences in the scatter of the two 

 groups is also significant as measured by the standard devia- 

 tion. The standard deviation for the Holstein-Friesian group 

 is 0-3i8±.oo4 and that of this Jersey group is 0.440^.005 or the 

 difference and the probable error are 0.131^.006. Absolutely 

 •considered the higher fat test cows are more variable than the 

 lower butter-fat percentage cows. In the Jersey or highest 

 group no influence of age on the standard deviation appears to 

 exist. 



The coefficient of variation is worth especial study as it 

 gives us in comparable terms the relation between the standard 

 deviation of a distribution and its mean. For our problem the 

 conclusions to be derived from it are not, unfortunately, so 

 straight forward as we are dealing with the index, butter-fat 



