52 Economic Cycles: Their Law and Cause 



it must be eliminated before the fluctuation is com- 

 puted. 



In Table III of the Appendix to this chapter the 

 fluctuation for each of the forty-one years 1870-1910 

 is given for corn, oats, hay, and potatoes. By taking 

 the algebraic sum of the fluctuations for all the crops 

 for any given year and dividing by four — the number of 

 the crops — a measure of the fluctuation of the crops 

 taken all together is obtained. This measure we shall 

 refer to as the index of the fluctuation of crops. The 

 index for each of the years 1870-1910 is recorded in the 

 last column of Table III. 



The index of crop fluctuation computed in the man- 

 ner that has just been described is regarded as a more 

 accurate measure of the fluctuation of crops than 

 would be obtained from an index formed by taking as 

 the fluctuation for each year, in case of each crop, the 

 ratio of the deviation from the mean divided by the 

 mean. If the crops differ in their coefficients of varia- 

 tion, that is to say, if the ratio -^, where M is the mean 



yield and cr is the standard deviation, is not the same 

 for all crops, then the crop with the largest coefficient of 

 variation would receive the largest weight in the general 

 index. The coefficients of variation for the crops in 



our Table are, for corn, ^-f— =.217; for oats, —-— = 



2b. 93 31.44 



1 8 9*3 9^ 



.164; for hay, —^ = .137; for potatoes, ^^ = .330. If 



the usual method of forming index numbers were em- 

 ployed in this case to measure crop fluctuations, the 



