galton.org 35
Statistical Methods
35
quality in the corresponding objects, then their shape will always resemble
that shown in Fig. 1.
The form of the bounding curve resembles that which is called in
architectural language an ogive, from “augive, an old French word for a
cup, the figure being not unlike the upper half of a cup lying sideways
with its axis horizontal. In consequence of the multitude of mediocre
values, we always find that on either side of the middlemost ordinate Cc,
which is the median value and may be accepted as the average, there is a
much less rapid change of height than elsewhere. If the figure were pulled
out sideways to make it accord with such physical conceptions as that of a
row of men standing side by side, the middle part of the curve would be
apparently horizontal.
The mathematical conception of the curve is best expressed in Fig. 2.
where PQ represents any given deviation from the average value, and the
ratio of PO to AB re resents the relative probability of its occurrence. The
equation to the curve and a discussion of its properties will be found in the
Proceedings of the Royal Society, No. 198, 1879, by Dr. M’Alister. The
title of the paper is the “Law of the Geometric Mean,” and it follows one
by myself on “The Geometric Mean in Vital and Social Statistics.”
We can lay down the ogive of any quality, physical or mental,
whenever we are capable of judging which of any two members of the
group we are engaged upon has the
