150 



Pearl and Surface. 



Table 16. 



Frequenc.v Distrilmtioii of the Meau Quiutile Position of 



Individual Plants. 



being multiplied by the unit of grouping (0-8 quintile in tliis case). 

 The standard de\iation in class units represents the variation without 

 reference to the grouping. It is the same as if the classes had the 

 value of 1, 2, 3, 4, and 5. 



Now it can be shown by simple algebra that if the variates are 

 equally distributed among the classes the standard deviation in class 

 units will be the same as for the first n natural members, in which case 



Il2— 1 



When n is equal to 5, 



Ö = VI = 1-4142. 

 This would be the standard deviation if the obseivatious were 

 equally distributed in all five classes. By comparing tliis value with 

 the constants in the last column of table 16 it is seen that tlie ob- 

 served values are rather close to the theoretical constant. For series B 

 the agreement is very close, the difference being only about one-seventh 

 of the probable error. In no case does the observed value deviate 

 fiom tlie theoretical value as much as three times its probable error. 

 Thus, none of the observed standard deviations are certainly 

 significantly different from the standard deviation of a dis- 

 tribution in which the variates are equally distributed among 

 the classes. However, all the observed values deviate from the theo- 

 retical in the same direction. This fact is probably significant and in- 

 dicates that there is some fundamental cause which produced a frequency 



