THE MEASUREMENT OF VARIATION. 17 



especially those belonging to the Animal Kingdom, 

 the variations are distributed about their mean in 

 accordance with the Law of Error. It is scarcely 

 necessary to point out, however, that the actual 

 range of the variations is exceedingly variable, and 

 that the general contour of the curves, supposing 

 the results are expressed in that way, must be equally 

 variable. The greater the variability of any char- 

 acteristic, the more spread out, or flattened, must be 

 the curve representing the frequencies of its devia- 

 tions. If, therefore, results were invariably expressed 

 in the form of curves, and if, by multiplying each 

 series of measurements by some factor, the central 

 ordinate were always brought to the same height, 

 then it would follow that the variability of each char- 

 acteristic would be accurately represented by the ex- 

 tent of spread of the curve. In order to obtain an in- 

 dex of the variability of any characteristic, we must 

 accordingly adopt some convenient method of deter- 

 mining the degree of spread of its curve. One of the 

 simplest of these methods, and one widely employed by 

 English statisticians, is to determine the so-called 

 Probable Error. The meaning of this term is best 

 explained by reference to the accompanying diagram of 

 a curve of frequency of error. The ordinate drawn 

 through the middle of the curve is spoken of by Mr. 

 Galton as the Median, and is denoted by the symbol M. 

 In symmetrical curves it is identical with the ordinary 

 arithmetic mean or average, and in this sense is called 

 the Centroid Vertical. It is the middle value of the 

 whole series of observations, which are symmetrically 

 distributed on each side of it. That is to say, 50 per 



