RELIABILITY AND ADEQUACY OF FARM-PRICE DATA 25' 
of more than 10 per cent in States of surplus production. Oat prices 
in Missouri, Illinois, and Indiana for June, 1925, showed a coefficient 
of variability of 11.7, 11.9, and 11.6 per cent. The prices of all ha} 7 , 
milk cows, and horses are much more variable, with coefficients of 
variability ranging from 25 to 30 per cent or more. 
The prices of many farm products are much more variable in 
Southern States than in Northern States. Coefficients of variability 
of Georgia prices in November, 1925, were: Corn, 19 per cent; sweet 
potatoes, 32 per cent ; eggs, 14 per cent ; and chickens, 18 per cent — 
all nearly three times as large as the same products in Northern 
States. On the other hand, variability of hay prices was about 
the same in Georgia as in New York or Indiana, and the same was 
true of prices of milk cows. 
The next step is to measure the relative reliabilit}^ of the average 
of the same sample when the variability and the number of reports 
are known. The probable error of the average mean is used for 
this purpose. This is found by dividing the standard deviation of 
the sample by the square root of the number of reports and multiply- 
ing by 0.6745. The probable error signifies that the chances are 50 
out of 100 that the average of an indefinitely large sample collected 
in the same way as the given sample would not vary more than the 
amount of the probable error from the average of the sample we 
have. Owing to the probabilities of sampling the chance of an 
average being more inaccurate than four times its probable error 
is but 1 in 100. To compare the probable error of various price 
samples, a new statistical term has been improvised known as the 
"relative probable error." It is obtained by expressing the prob- 
able error as a percentage of the average, just as the coefficient of 
variability is the standard deviation of the sample expressed as a 
percentage of the average. 
The probable errors of hog prices per 100 pounds in Iowa for 
several different months during 1924 and 1925 were as low as 3 
cents in one month and as high as 9 cents in another. It is custom- 
ary to round the hog prices to the 10-cent interval. The relative 
probable error for these samples ranged from 0.3 to 0.9 per cent. 
The relative probable error of the Kansas wheat price in October, 
1924, with only 35 reports, was 0.7 per cent ; in June, 1925, when there 
were 106 reports, it was 0.3 per cent; that of the price of eggs in 
Nebraska in May, 1925, with 118 reports, was 0.4 per cent; that of 
the price of South Carolina cotton in October, 1924, with 40 re- 
ports was 0.6 per cent. In other words, the chances are 99 out of 
100 that the average of a larger sample taken in the same way as 
this one would have been within 2 per cent of the one obtained, or 
four times the relative probable error of 0.5 per cent. 
If we take 0.5 per cent relative probable error or 2 per cent (four 
times the relative probable error) as our goal of desired accuracy, or 
reliability, how many reports will be necessary with samples of dif- 
ferent variability? With a coefficient of variability of 5 per cent, 
about 45 reports would be necessary to obtain a relative probable 
error of 0.5 per cent ; with a coefficient of variability of 10 per cent, 
about 180 reports would be necessary; with a coefficient of variabil- 
ity of 20 per cent, about 730 reports would be necessary and with a 
26813°— 27 4 
