NORMAL VARIABILITY QI 
extraction; and exhibits in a concise form the result of 
4,426 measurements recorded by the Cambridge Anthro- 
pometric Society. In this figure the stature in inches is 
indicated on the base line, whilst the perpendicular 
distances indicate the number of cases in which each 
particular height was recorded. The separate classes 
in this case include those who were found to fall within 
the limits of 4 inch on either side of each consecutive 
integral inch of stature, measurements which fell 
exactly half-way between two classes—e.g., one of 
693 inches—being reckoned as a half to each of the 
classes in question. The continuous line in the diagram 
represents the form of the ‘normal curve’ which 
approximates most nearly to the line obtained by 
joining together the points actually plotted. 
There seems to be good evidence that in such a case 
as that of human stature the figure obtained in this way 
will approximate more and more closely to the shape 
of what is known as a normal curve, according as the 
number of individuals measured and the accuracy of the 
measurements increase. 
In order to arrive at a proper understanding of this 
fact, we must consider the derivation of the ‘normal’ 
curve from another point of view—namely, from the 
point of view of the mathematical theory of proba- 
bility, which it will be our endeavour to present in as 
simple a manner as possible. 
Let us consider the result of tossing up a number 
of similar coins simultaneously. If we toss up two 
coins only we may get any of the following results : 
(1) Head head, (2) head tail, (3) tail head, (4) tail tail. 
