Page:Popular Science Monthly Volume 78.djvu/415

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the cases lie. It means that a student taken at random from a class of one hundred has one chance in four of falling above the middle group. It means that if we represent the ability of this group by C, we know precisely what an instructor means when he gives a student that grade. He means that the ability of the student in his course is greater than that of one fourth of the course and less than that of another fourth of the course. This median group ought to be the largest, for it is where most human beings fall, as shown by the height of the probability curve.

We can not indicate real distinction, however, unless we subdivide the upper quartile. We can do this arbitrarily or we can turn to a table of values of the normal probability integral.[1] Here the extreme ability is called 3. The point of the vertical line which separates the median group from the inferior group is .68. Half way between 3 and .68 is 1.84. Accepting this as the division point for the upper and the lower quartile, we find at the upper end of the surface of distribution three per cent, of the whole, and at the lower end three per cent. If we indicate the five sections, from the upper end to the lower, by the symbols A, B, C, D, E, we have the following distribution of grades:

Per Cent.
A 3
B 22
C 50
D 22
E 3

If, on the other hand, we assume that the distribution of abilities of college students is not normal, but skewed, the following percentages for each grade would more nearly represent the facts:

Per Cent.
A 2 20
B 18
C 50
D 24 30
E 6

As variation in the abilities of those who elect a given course is sure to occur from year to year, some would prefer an elastic definition of the grades; for example:

Per Cent.
A 0-6
B 15-21
C 45-55
D 20-28
E 0-10
  1. A table of values of the normal probability integral is found on page 148 of Thorndike's "Mental and Social Measurements." In Science, 712, 243, Max Meyer uses this basis for dividing the probability surface.