546 JOURNAL OF FORESTRY 



three columns appears to show that both A B and C D are satisfactory 

 in their position, while columns 4 and 5 bring out the actual marked 

 inferiority of C D. 



This is merely a hypothetical case, but it indicates how the aggregate 

 check, while essential, may be misleading if used alone. The optimum 

 position of any curve is that which not only gives a negligible difference 

 in the aggregate but also a minimum sum (or average) of all the devia- 

 tions of its basic points therefrom. 



This statement is of course not strictly accurate. By the theory of 

 least squares the best possible fit of a given line or curve to empirical 

 data is that which gives a minimum sum of the deviations squared. To 

 square all the deviations, however, is laborious and may be an unneces- 

 sary refinement. These considerations open up the question of which 

 of the commonly recognized "measures of dispersion" ^ should be em- 

 ployed in the case of volume tables. There are three which seem 

 particularly promising, the probable error of the mean, the standard 

 deviation, and the average deviation. The former is attractive in the 

 implication of its name which loses, however, some of its significance 

 when applied not to a simple arithmetical average but to an average 

 curve of unknown equation. Its formula is relatively complicated and 

 the resulting additional labor seems unjustified. The standard devia- 

 tion (that is, the square root of the average squared deviation) is an 

 accurate criterion as above indicated, but its computation is laborious 

 and it is to be avoided if possble. The average deviation is far simpler 

 and seems to be sufficiently accurate. It can be proven that the average 

 deviation is a minimum when figured from a median value rather than 

 from an arithmetical mean. In any case where median and arithmetical 

 mean coincide it is, then, just as accurate as the standard deviation. As 

 a matter of fact in the case of volume tables, there are strong indica- 



' See such works as "An Introduction to the Theory of Statistics," by G. N. 

 Yule, for a complete general discussion thereof. 



