In the long
run, the greatest number of his shots would be in the picket aimed at,
and of his misses there would be just as many on one side as on the
other, just as many above as below the center. Now if all the shots, as
they struck the fence, could drop into a box below, which had a
compartment for each picket, it would be found at the end of his
practice that the compartments were filled up unequally, most bullets
being in that representing the middle picket and least in the outside
ones. The intermediate compartments would have intermediate numbers of
bullets. The whole scheme is shown in Fig. 11. If a line be drawn to
connect the tops of all the columns of bullets, it will make a rough
curve or graph, which represents a typical chance distribution. It will
be evident to anyone that the distribution was really governed by
"chance," i.e., a multiplicity of causes too complex to permit detailed
analysis. The imaginary sharp-shooter was an expert, and he was trying
to hit the same spot with each shot. The deviation from the center is
bound to be the same on all sides.
[Illustration: 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.
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