CHAPTER XII 

 Age of the Cow in Relation to Milk Yield 



The collection of data for this subject requires so much effort 

 that the student must, practically speaking, take the scatter table 

 of others for granted. For illustrative purposes, I take the tables 

 for the relation of 365-day Guernsey milk yield with age. This is 

 the ordinary correlation table used to show the relation of one 

 variable to another (see page 78). 



The way in which such a table is made is as follows : Cards show- 

 ing these records are first sorted into age groups of six months, be- 

 ginning at one year and six months. These groups represent the 

 frequency distribution shown under "Total" at the right. They 

 are then sorted for the milk yield groups as shown above the table. 

 The frequency distribution for each age is consequently the vari- 

 ation of milk yield for each six months of age. 



If milk yield is related to age, the mean milk yields would be 

 expected to rise or fall in some definite manner with increase in age. 

 To get the mean milk yields for the age groups we adopt the method 

 of arbitrary origins and call each class an increase of unity over the 

 preceding class. The top line marked X shows these classes. The 

 S(x) (summation x) of each row is found by multiplying the number 

 in the row by the class unit in X and adding. Thus for the first 

 row: 



(7X1) + (44 X 2) + (69 X 3) + (52 X 4) + (42 X 5) + (17 X 6) + (9 X 7) 

 + (3 X 8) + (1 X 9) = 918 



The mean milk yield of the first row may be obtained from this 

 data by the following method: 



918 s(x) n „ nnn „ 



= = 3.762295 



244 n 



or in other words the mean milk yield of the row is 3.762295 units 

 away from our arbitrary origin. Now each unit is equal to L000 



77 



