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
Fig. 1.
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
