32 



THE MEASUREMENT OF VARIATION. 



abscissa much more rapidly on one side than on the 

 other, and so, for practical purposes, by taking various 

 values for p, q, and n, we can represent series of the 



05 



1 234 5 6 S 8 9 IX) U 12 



FIG. 5. Types of binomial curves. (After Duncker.) 



following five types by means of the above generalised 

 expression: 



I. Asymmetrical curves limited on both sides. 

 II. Symmetrical 



III. Asymmetrical " " " one side, unlimited on the other. 



IV. Asymmetrical curves, unlimited on both sides. 

 V. Symmetrical " 



The normal curve of error belongs to this last type. 

 Pearson has also pointed out that the abnormal fre- 

 quency curves which cannot be represented by a point- 



