TYPE AND VARIABILITY 



441 



If another distribution should give a smaller E, we should con- 

 clude that more confidence could be reposed in this second 

 determination than in the first. 



Obviously will decrease as the standard deviation de- 

 creases or as the numbers examined increase (see formula). Our 

 numbers are relatively small (327) and our probable error is 

 relatively high, though it constitutes but an insignificant frac- 

 tion of the determination (1.28). 



Probable error of coefficient of variability. When the coeffi- 

 cient of variability (C) is small (10 per cent or less) its probable 

 error is found by dividing the coefficient of variability by the 

 square root of twice the number of variates and multiplying by 

 0.6745 ; that is, by the same formula as the one just given, 

 only substituting coefficient of variability for standard devia- 

 tion. 1 When the coefficient is larger than 10 per cent we use 

 a slightly more complicated formula. 2 



Since the variability in question (14.5) is greater than 10 per 

 cent we employ the more extended formula and obtain the 

 following : 



c = 0.6745 



The student will find on trial that for these values the two 

 methods give results but slightly different. 



Deviation and probable error illustrated. This whole matter 

 of deviation and probable error is well illustrated in shooting 

 at a mark. Some of the shots will strike the bull's-eye and 

 others will strike at various distances from the center, some 

 going wild. Obviously the better the shooting the closer will 

 the shots be clustered about the bull's-eye. The distance of 

 each shot from the center would be its deviation from the 

 mark and the mean of all the deviations of the marksman A 

 would represent the average of his deviations. 



f* 



1 Formula E c = 0.6745 



= 0.6745 I i + 2 / J . See C. B. Davenport, Statistical 

 Methods, p. 1 6. ^ L 



