Fig. 11.—The "Chance" or "Probability" Form
of Distribution.
Now suppose a series of measurements of a thousand children be taken in, let
us say, the ability to do 18 problems in subtraction in 10 minutes. A few of
them finish only one problem in that time; a few more do two, more still are
able to complete three, and so on up. The great bulk of the children get through
from 8 to 12 problems in the allotted time; a few finish the whole task. Now
if we make a column for all those who did one problem, another column beside
it for all those who did two, and so on up for those who did three, four and
on to eighteen, a line drawn over the tops of the columns make a curve like the
above from Thorndike.
Comparing this curve with the one formed by the marksman's
spent bullets, one can not help being struck by the similarity. If the first
represented a distribution governed purely by chance, it is evident that the
children's ability seems to be distributed in accordance with a similar law.
With
the limited number of categories used in this example, it would not be possible
to get a smooth curve, but only a kind of step pyramid. With an increase in the
number of categories, the steps become smaller. With a hundred problems to work
out, instead of 18, the curve would be something like this:
