APPENDIX 



The formula for this is simply 



701 



where the marks | j indicate that the numbers should all be taken with the 

 positive sign. 



This measure of variability is usually known as the average deviation. 



As to the relative merits of these two measures of variability, the stand- 

 ard deviation is to be preferred. Its relation to the probability curve as 

 indicated above gives it special favor mathematically, although a geometric 

 meaning may also be given to the average deviation. 



Probable error of the mean. Since in natural science results are, in gen- 

 eral, based on averages, we are more directly interested in the probable 

 error in the mean than in the probable error of a single variate, although 



the latter conception is desirable as a basis for understanding the former. 

 We can best discuss the probable error in the mean by beginning with an 

 illustration. 



Suppose that, in determining the average stature of a male population 

 consisting of a million individuals, we select at random groups of a thou- 

 sand each. We could then, in all, have available a thousand such groups 

 using no individual twice. It is an axiom of statistics, as we have already 

 explained, that the mean statures obtained from each of these groups will 



