Now, as it happens, hog receipts are a much more violently fluctuating series than bank clearings outside of New York City. To put the series on an even footing, resort is made to what is known as the standard deviation. To secure the standard deviation of hog price percentage departures, add up the squares of these departures. The total for the 168 months from 1903 thru 1916 is 31,894, or, dividing by 168, we get 190. The square root of 190 is 13.8, which is the standard deviation of hog prices. Standard deviation means that the probabilities are that on the average not more than one out of three of the series of figures under consideration will exceed the standard deviation. Standard deviation for hog receipts is 15, and for bank clearings 8.7. This indicates that hog receipts depart from the secular trend as modified seasonally with nearly twice as great violence as do bank clearings. To put all three series on the same footing, we divide the percentage departures by the standard deviation, 13.8 in the case of hog prices, 15 in the case of hog receipts, and 8.7 in the case of bank clearings. In January of 1903, for example, hog prices were greater than the secular modified seasonally by 2.3 times the standard deviation; hog receipts were less by .3 of the standard deviation, and bank clearings were over by .9 of the standard deviation. The cycles of the hog prices, hog receipts and bank clearings, as secured in this way by reducing for standard deviation, are comparable. The results are charted in Charts III, IV, V. [Illustration: Chart I—Irregular line represents actual Chicago hog prices. Straight line represents secular trend. ] [Illustration: Chart II is identical with Chart I except that the dotted line has been added, which represents the secular trend as corrected seasonally. ] It may be seen from examining these charts that hog prices seem to be related directly to bank clearings and inversely to hog receipts. The problem is: Blend hog receipts and bank clearings together in such a way as to secure hog prices. The mathematical method of approach is by correlation coefficients and lines of regression. First, a simple illustration of the method of securing correlation coefficients: Take the two series, A and B, which deviate from their respective means by the amounts stated in Columns 2 and 3. In Column 1 is the year, which has nothing to do with the mathematics of the case. Column 4 is A squared, Column 5 is B squared, and Column 6 is A multiplied by B.