bblestones, the deviations from the
bull's-eye in a target-shooting contest, or by plotting the
variability of any organismal character--whether it be the stature or
strength of men, the spread of sparrows' wings, the number of rays on
scallop shells, or of ray-flowers of daisies.

[Illustration: FIG. 4.--Model to illustrate the law of
probability or "chance." Description in the text. _A_, Peas
held in container at top of board. _B_, Peas after having
fallen through the obstructions into the vertical
compartments below. The curve connecting the tops of the
columns of peas is the normal probability curve.]

With this model we may illustrate many other essential facts about
variability which must be borne in mind when approaching the problems
of Eugenics. Before we allow the peas to fall we know quite definitely
what the general distribution of them all will be, but we do not know
at all the future position of any single pea. Of this we can speak
only in terms of probability; the chances are very high that it will
fall in one of the three middle compartments, very low that it will be
in one of the extreme compartments. But the chances are equal,
whatever they are, that it will fall above or below the average or
middle position. We see then that in any group there are many more
individuals near the average, i. e., mediocre, than there are in the
classes removed from the average and the farther the remove of a class
from the average the smaller the number of individuals in that class.
Yet all the individuals belong to the same whole group. This leads to
the very important fact that _an individual may belong to a group
without representing it fairly_. The average individuals are the most
representative. But in order to get a correct idea of the whole group
we must know, first, to what _extent_ deviations occur in each
direction, above and below the group average, and, second, the average
_amount_ by which each individual of the group deviates from this
group average. That is, we must know the amount of variability as well
as the extent of the greatest divergence from the average. The best
measure of the amount of variability exhibited by any group of objects
or organisms is not the simple average or mean of all the individual
deviations from the average of the group; it is the square root of the
mean squared deviations from the group average. This is called the
_index_ of variability or "standard de