THE MEASUREMENT OF VARIATION. 33 



binomial may be the resultant of two or more normal 

 curves, which differ in the position of their axes, or 

 their areas, or their degree of spread, or in all three of 

 these respects.* 



To return to the curves in Fig. 5, we see that the 

 centroid vertical of the symmetrical curve corresponds 

 to the summit of the curve, or is identical with the 

 maximum ordinate or mode, as it is sometimes called. 

 In the asymmetrical curves, however, this is not the 

 case, but the more asymmetrical the curve, the greater 

 is the distance between the two. The ratio between 

 this distance and the index of variability adopted (such 

 as the error of mean square), gives a convenient " index 

 of asymmetry ' ' of the curve. It is to be noted also 

 that in asymmetrical curves the median, or middle 

 value of the whole series, such that 50 per cent, of the 

 values are below it in magnitude and 50 per cent, above 

 it, no longer coincides with the arithmetic mean. It 

 lies somewhere between the centroid vertical and the 

 maximum ordinate. 



As to the practical application of this method of fit- 

 ting series of variation frequencies with curves, Pro- 

 fessor Pearson gives numerous instances in the above 

 cited memoir. Fig. 6 will serve to afford some idea as 

 to the types of frequency curves actually met with in 

 practical statistics. Type represents the above-men- 

 tioned series of frequencies which De Yries obtained for 

 the petals of buttercups, and high blossoms of clover. 

 It also represents infantile mortality statistics. Type /3 

 represents the relation of scarlet fever and diphtheria 

 mortality to age; type y that of scarlet fever and 



*Proc. Roy. Soc., liv. p. 329. 



