VARIABILITY OF A SINGLE CHARACTER 107 



Frequency distributions are always characterized by a gradual 

 rise to the mode and then by a corresponding fall. This " slope " 

 of the frequency is best brought out to the eye by the system of 

 plotting, in which the distribution is put into the form of a 

 curve, called everywhere the frequency curve (see Fig. 17). 



To plot this curve lay off the horizontal line X'X, and erect 

 O Fas a perpendicular. Next lay off distances on X'X both ways 

 from O, corresponding to the scheme of values, and erect perpen- 

 diculars from each. Then lay off on Fa distance correspond- 

 ing to the modal value, — in this case 59, — and on each of the 



5.0 



G.5 7.0 7.5 8.0 9.0 9.5 10.0 10.5 11.0 11.5 

 Fig. 17. The frequency curve 



perpendiculars a distance corresponding to the number it repre- 

 sents. Last of all, connect these points with a curved line, and 

 this line will be the so-called curve of frequency, which is a true 

 picture of the variability of the character in question. 



A glance at Fig. 17 will show that this distribution is not 

 quite as smooth as would be desired, — a fault that would be cor- 

 rected with a larger number of ears, in which case the slopes of 

 the curve would be more regular and its character more uniform. 



The mean. It is clear that two populations x might have the 

 same mode but with very different distributions. There is there- 

 fore another conception of type quite aside from the highest 



1 " Population " is the technical term for the group of individuals studied, 

 whether corn or cattle or people. In the present instance we are trying to 

 study the variability as to length of ear in Reed's Yellow Dent, which is the 

 population, by means of a supposedly random sample of 286 ears — rather too 

 few for smooth results, but upon the whole fairly satisfactory. 



