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:
[Illustration: FIG. 12.--Probability curve with increased
number of steps.]
And with an infinite number, the steps would disappear altogether,
leaving a perfectly smooth, flowing line, unmarred by a single step or
break.
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