portional to the number of women falling within the limits of an inch. Thus 16.3 per cent, were between 63 and 64 inches; 11.5 per cent, between 64 and 65 inches, etc., only two falling between 70 and 71 inches. The women near the average tend to differ in height by about 1/200th of an inch, while the tallest or shortest of the thousand tend to differ by half an inch or more. This curve, showing the
distribution in height, corresponds closely with the fainter and more regular curve on the figure which represents the distribution of events due to a large number of small causes equally likely to affect them in one of two ways, the curve of error of the exponential equation whose properties have been discussed by Gauss, Laplace and other mathematicians.
If the performances of students in examinations are assumed to vary in the same way as their height, then we can if we like place them in classes which represent equal differences. Thus by the Harvard-Columbia method of grouping into five classes, if we put half the men into the middle class, C, and let B and D represent an equal range, we should give about 23 per cent, of both B's and D's and about 2 per cent, of both A's and F's. This, however, gives too few men in the A and F classes for our purposes. If we make the range of the unit 20 per cent, smaller, we obtain the distribution shown in Figure 3, according to which of ten men four would receive C, two B, two D, one A and one F. It departs slightly from the theoretical distribution, but certainly not so much as the theoretical distribution departs from the actual distribution. It appears to be the most convenient classification when five grades are used; one in ten being given honors and one in ten being required to repeat the course corresponding fairly well with the average practise and being a convenient standard.
