: THEORY OF STATISTICS. 
Nelumbiwm, Pearl, American Naturalist, Nov. 1906). The question 
arises,” therefore, why, in such cases, the distribution should be 
approximately normal, a form of distribution which we have only 
shown to arise if the variable is the sum of a large number of 
elements, each of which can take the values 0 and 1 (or other two 
constant values), these values occurring independently, and with 
equal frequency. 
In the first place, it should be stated that the conditions of the 
deduction given in § 9 were made a little unnecessarily restricted, 
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Stature tn inches, 
Fig. 49.—The Distribution of Stature for Adult Males in the British Isles 
(fig. 6, p. 89), fitted with a Normal Curve: to avoid confusing the 
figure, the frequency-polygon has not been drawn in, the tops of the 
ordinates being shown by small circles. 
with a view to securing simplicity of algebra. The deduction 
may be generalised, whilst retaining the same type of proof, by 
assuming that p and ¢ are unequal (provided p—g¢ be small 
compared with Jpg, of. § 3), that p and ¢ are not quite the 
same for all the events, that all the events are not quite inde- 
pendent, or that » is not large, but that some sort of continuous 
variation is possible in the values of the elementary variables, 
these being no longer restricted to O and 1, or two other discrete 
values. (Cf. the deduction given by Pearson in ref. 13.) Pro- 
ceeding further from this last idea, the deduction may be rendered 
306