NORMAL VARIABILITY 91 



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 -J- inch on either side of each consecutive 

 integral inch of stature, measurements which fell 

 exactly half-way between two classes e.g., one of 

 69^ 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 : 

 (i) Head head, (2) head tail, (3) tail head, (4) tail tail. 



