26 
coefficient of variability of 30 per cent, 1,640 reports would be 
necessary to obtain a relative probable error of 0.5 per cent. If 
we are willing, however, to be content with a relative probable error 
of about 2.5 per cent, or practical certainty within a range of 10 per 
cent (four times the probable error) for the prices of the less im- 
portant crops, or crops of minor importance within a State, a 
small number of reports will be sufficient. Even when the coefficient 
of variability is 30 per cent, a 64-report sample will give a probable 
error of 2.5 per cent. 
ANALYSIS OF PRICES OF FARM CROPS 
The succeeding tables (Tables 9 to 22) show the number of re- 
ports, the average price, the standard deviation of the reports, the 
coefficient of variability, the probable error of the average price 
or mean, the relative probable error, and four times the relative 
probable error of several samples of farm-price data for a number 
of farm crops for various States. 
For the sake of comparison, prices of all of the farm products 
shown have been considered on the basis of random or simple 
sampling, with a straight, unweighted average for each State. 
The probable error of the weighted average would be larger than 
the probable error of the straight average of a sample of the same 
size. On the other hand, the probable error of the average used 
is reduced bv the fact that the sample is selected bv crop-reporting 
districts and counties (11, p. 349), (3, p, 316, 337), 
Table 9 shows a comparison of the size of the wheat-price sam- 
ple, the dispersion, variability, and probable error of the average 
price obtained for several different States. This table includes 
the December 1 price for Kansas and Maryland as obtained from 
crop reporters on the township list, and for Kansas the value per 
bushel of the 1924 crop of wheat whether sold or to be sold, by 
crop-reporting districts, as determined from a special inquiry, 7 
addressed to the township and field-aid lists of crop reporters. 
The price of wheat shows as little variability as the price of any 
other farm product. In an ordinary year there is not a wide range 
of prices in a winter-wheat State like Kansas. Freight rates, 
quality, and protein content are important factors causing variation 
in the price reports received. In a State like Xorth Dakota, where 
the durum wheat is on an export basis and the other spring wheat 
is on an import basis, as was the case in the 1925-26 season, there 
may be a very wide range in prices. In reality, the sample shows 
two modes, one for the durum wheat and one for other wheat. 
7 Part of a special-price inquiry made by the department in March, 1925, in all States 
on crops, livestock, and livestock products. The prices or values determined from this 
inquiry were furnished to the Bureau of the Census for use in evaluating the production 
of 1924 by counties. Farm prices are not regularly obtained on a scale warranting 
publication for smaller units than a State. The complete series by crop-reporting districts 
obtained in this special inquiry is given in Statistical Bulletin 14—17. For crops, corre- 
spondents were asked to report the average value or price per unit for the season, whether 
sold or to be sold, 
