Ill 



OF VARIABILITY 



119 



statistical study of Variation, led Francis Galton to enquire into 

 the laws of Natural Inheritance, and served Karl Pearson as the 

 foundation of his science of Biometrics. 



When Quetelet tells us that the mean stature of a ten-year-old 

 boy is 1-275 metres, this is found to imply, not only that the 

 measurements of all his ten-year-old boys group themselves about 

 this mean value of 1-275 metres, but that they do so in an orderly 

 way, many departing httle from that mean value, and fewer and 

 fewer departing more and more. In fact, when all the measure- 

 ments are grouped and plotted, so as to shew the number of 

 instances (y) ^ each gradation of size (x), we obtain a characteristic 



-2cr —cr 



Fig. 21. The normal curve of frequency, or of error. 

 a, -a, the "standard deviation". 



configuration, mathematically definable, called the curve of frequency, 

 or oi error (Fig. 21). This is a very remarkable fact. That a "curve 

 of stature" should agree closely with the "normal curve of error" 

 amazed Galton, and (as he said) formed the mainstay of his long 

 and fruitful enquiry into natural inheritance*. The curve is a 

 thing apart, sui generis. It depicts no course of events, it is no 

 time or vector diagram. It merely deals with the variabihty, and 

 variation, of magnitudes; and by magnitudes " we mean anything 

 which can be counted or measured, a regiment of men, a basket of 



* Stature itself, in a homogeneous population, is a good instance of a normal 

 frequency distribution, save only that the spread or range of variation is unusually 

 low; for one-half of the population of England differs by no more than an inch 

 and a half from the average of them all. Variation is said to be greater among the 

 negroid than among the white races, and it is certainly very great from one race 

 to another: e.g. from the Dinkas of the White Nile with a mean height of 1-8 m. 

 to the Congo pygmies averaging 1-35, or say 5 ft. 11 in. and 4 ft. 6 in. respectively. 



