16 BTLLEIIX 1372, U. S. DEPARTMENT OF AGRICULTURE 
Thus sires Q and T, who decreased the average butterfat yield of 
their daughters, have a higher ra nk ing than do sires M, O, and P, 
who increased the average butterfat yield of their daughters. This 
is brought about largely through the much higher average yield of 
miik and butterfat of the daughters of the sires Q and T 7 though the 
relative ranking among these five sires in the percentage of daughters 
better than then dams is high for sire Q in Doth milk and butterfat 
and for sire T in milk. 
Such inconsistencies do not appear in the rankings of the other 
sires, though the final ranking is not always in the same order as the 
amount of the average increase or decrease of the daughters for any 
one class. 
THE STANDARD DEVIATION AND COEFFICIENT OF VARIABILITY FOR BUTTERFAT YIELD 
OF THE DAUGHTERS OF THE 23 SIRES AND OF THFJR DAMS 
Judging by the records of the daughters of the 23 sires in this study, 
it is not to be expected that any sire, at this stage of breed improve- 
ment, will get daughters all of which will have the capacity to make 
uniform records of any certain standard. This is true regardless 
of how uniform the production records may be of the dams to which 
a sire is mated. A study of the detailed records given in Table 2 
readily shows the great variation in the producing capacity of 
each sire's daughters. It is not strange that there should be such 
a great variation when the double nature of the hereditary make-up 
of each individual is considered and when we realize how few matings 
are made where the animals are known to be homozygous or pure 
in their inheritance for the desired characters. If a sire's inheritance 
for a character, such as milk and butterfat producing capacity, is 
not homozygous, so that he can not transmit to each of his offspring 
the same capacity for production, and then if this sire is mated to a 
group of dams, each of whose 30 ancestors in 4 ancestral generations 
show varying degrees of producing capacity, it is not surprising that 
the offspring should show a wide variation in producing ability. 
It would seem that a prepotent she, matea to a group of cows 
having a considerable range in producing capacity, would get 
daughters showing greater uniformity of production. The standard 
deviation 3 and the coefficient of variability of the butterfat yields 
of daughters, and of their dams, as given in Table 7, does not show 
that the sires who decrease the coefficient of variability were any 
more prepotent in increasing production as measured in Table 5, 
than were the sires who increased the variability of the butterfat 
producing capacity of their daughters. The dams to which sire N 
was mated had a standard deviation of 148 pounds butterfat, whereas 
his daughters had a standard deviation of only 76 pounds butterfat — 
a decrease in the coefficient of variability from 25.22 per cent for 
the dams, to 12.57 per cent for the daughters. Yet sire N ranks 
thirteenth in prepotency for producing capacitv as measured in 
Table 5. 
On the other hand sire Is daughters show a standard deviation of 
170 pounds butterfat as compared with a standard deviation of only 
62 pounds butterfat in their dams. The coefficient of variability is 
increased from 11.56 per cent for the dams to 26.91 per cent for the 
3 "Standard deviation" is a term used in statistical calculations to denote a mathematical measure of 
the variability of the" items in a group from the mean, or average, of the whole group. "Coefficient of 
variation" is an index of variability appearing in the form of rate per cent. 
