# Page:Popular Science Monthly Volume 81.djvu/458

452
THE POPULAR SCIENCE MONTHLY

We have:

 Mathematics 0 History 3 Literature 0 Science 3 Music 2 Drawing 1 Other hand-work 1 —— Sum of the seven differences 10

These facts are repeated in the first column of Table 3.

Table 3

 I Difference Be- tween El. Interest Rank and H. S. Interest Rank II Difference Be- tween El. Interest Rank and C. Interest Rank III Difference Be- tween H. S. Inter- est Rank and C. Interest Rank Mathematics 0 1 1 History 3 0 3 Literature 0 0 0 Science 3 1 2 Music 2 0 2 Drawing 1 0 1 Other hand-work 1 0 1 10 2 10

Computing the other differences as shown in the second and third column of Table 3, we have for this individual the means of answering question 1, concerning the permanence of interests. If the individual had remained unchanged in his interests from any one period to any other the appropriate seven differences of Table 3 would obviously have been all zeros and the sum of that column would have been zero. If, on the other hand, he had from one to another period, changed as completely as possible, the sum of the appropriate column of Table 3 would have been 24 (7-1, 6-2, 5-3, 4-4, 3-5, 2-6, 1-7 giving 24). If the individual's interests had been due to mere caprice, changing their relative strength at random, the sum of any column of Table 3 would approximate 16. For, if a 1 is equally likely to become a 1, 2, 3, 4, 5, 6 or 7, and so also of a 2, a 3, a 4, etc., the average result will be 16.[1]

Any quantity below 16 as the sum of a column then means some permanence of interests in the individual in question, and the degree of permanence is measured by the divergence from 16 toward 0.

For the permanence from the elementary-school period to the junior

1.  1 becoming 1, 2, 3, 4, 5, 6, 7 gives as differences 0, 1, 2, 3, 4, 5, 6; 2 becoming 1, 2, 3, 4, 5, 6, 7 gives as differences 1, 0, 1, 2, 3, 4, 5; 3 becoming 1, 2, 3, 4, 5, 6, 7 gives as differences 2, 1, 0, 1, 2, 3, 4.

Continuing and dividing the sum of the 49 differences by 49 we get 2 2/7 for the average difference by mere chance shifting and 7 X 2 2/7 or 16, as the average sum of a column in Table 3 by mere chance shifting.