CORRELATION" AS APPLIED TO FARM-SURVEY DATA. 3 
If, in two series of associated variables, as, say, the profit per 
head and the weight per head in the data under consideration, there 
is a tendency for a high value of the first to be associated with a 
high value of the second, the variables are said to be correlated, and 
the correlation is positive; while if a high value of the first is asso- 
ciated with a low value of the second, and vice versa, the correlation 
is said to be negative, and the best measure yet devised of the amount 
of the correlation is the so-called coefficient of correlation. In Table 
II is shown the calculation of the coefficient of correlation between 
profit and weight per head. 
The method is as follows : 
1. Find the average value for each of the variables. Here the, average 
profit per head is $0.78, and the average weight 834 pounds. 
2. Calculate the departure of the individual values from the average. In 
the case of record No. 1, the departure of the profit from the average is +$11.29, 
and of the weight, —49 pounds. 
3. Find the square root of the average of the squares of these departures. 
This is the so-called " standard deviation," and is a measure of dispersion or 
the amount of variability of each variable. 
4. Find the algebraic sum of the products of each pair of individual depart- 
ures, i. e., for each record, multiply the departure of the profit from the average 
by the departure of the weight from the average, and prefix the proper sign; 
then find the difference between the sum of all the plus products and the 
sum of all the minus products. 
5. Divide this result by the number of records and the standard deviation 
of each of the variables in turn, prefix the proper sign, and the figure obtained 
is the coefficient of correlation between the two factors under consideration. 
If there are approximately the same number of positive and nega- 
tive products and they are of the same size, it will be evident that 
there is no correlation, and this will be shown by the fact that the 
coefficient of correlation will be zero, or nearly so. If high values 
of the first variable are associated with high values of the second, 
and low values of the first with low values of the second, most of 
the products will be plus, and the greater their sum the closer will 
be the correlation and the larger will be the coefficient obtained. 
If a value of one variable below the average is generally associated 
with a value of the other above the average, the correlation will 
evidently be negative, and this will be shown by the fact that the 
sum of the products will be negative, the degree of the correlation 
and the size of the coefficient depending upon the size of this sum. 
Expressed algebraically, the coefficient of correlation, 
.■--?*-; (i) 
where Hxy is the sum of the products above mentioned, n is the num- 
ber of pairs of variables (the same as the number of records) ; a x 
