RELIABILITY AND ADEQUACY OF FAEM-PEICE DATA 
27 
Table 9. — Farm prices of wheat: Selected illustrations of size of sample, 
measures of dispersion, and prooable errors 
State, date, and district 
Number 
of 
reports 
Average 
price 
(arith- 
metic 
mean) 
Standard 
devia- 
tion of 
reports 
Coef- 
ficient of 
varia- 
bility 
Probable 
error of 
the aver- 
age price 
or mean 
Relative 
probable 
error 
Four 
times 
relative 
probable 
error l 
Kansas: 
October, 1924. . 
35 
120 
106 
30 
13 
23 
36 
119 
655 
77 
108 
84 
50 
89 
89 
• 50 
102 
94 
Cents per 
bushel 
122.0 
141.0 
150.0 
135.0 
155.0 
128.0 
164.5 
150.7 
147.2 
3 119.0 
3 122. 8 
3 125. 5 
3 119. 7 
3 120. 3 
3 119. 5 
3 122. 1 
3 119. 8 
3 121. 3 
Cents per 
bushel 
8.0 
11.0 
-8.0 
18.4 
7.0 
13.5 
8.7 
11.4 
8.4 
12.9 
15.3 
16.6 
17.1 
11.8 
18.9 
14.9 
13.2 
16.9 
Per cent 
6.7 
7.8 
5.3 
13.6 
4.5 
10.6 
5.3 
7.6 
5.7 
10.8 
12.4 
13.2 
14.3 
9.8 
15.8 
12.2 
11.0 
13.9 
Cents per 
bushel 
0.9 
0.7 
.5 
2.3 
1.3 
1.9 
1.0 
.7 
.2 
1.0 
1.0 
1.2 
1.6 
.8 
1.3 
1.4 
.9 
1.2 
Per cent 
0.7 
.5 
.3 
1.7 
.8 
1.5 
.6 
.5 
.1 
.8 
.8 
1.0 
1.3 
.7 
1.1 
1.1 
.8 
.9 
Per cent 
2.8 
April, 1925 
2.0 
June, 1925.. 
1.2 
Pennsylvania: 
October, 1924 
6.8 
April, 1925 
3.2 
Utah, November, 1925 . 
6.0 
Maryland: 
March, 1926. .. 
2.4 
Dec. 1, 1925 2 
2.0 
Kansas, Dec. 1, 1925 2 
.4 
Kansas, 1924, by crop-reporting 
districts: 
1 
3.2 
2 
3.2 
3 
4.0 
4 
5.2 
5 
2.8 
6... 
4.4 
7 
4.4 
8 
3.2 
9 . 
3.6 
State.. . 
743 
3 121. 1 
15.4 
12.7 
\ 4 0.377 
[ « 0.398 
.3 
* 0. 312 
» 0. 330 
1.2 
4 1.25 
•1.82 
i The probabilities are ninety-nine out of one hundred that the average of a much larger sample collected 
in the same way and at the same time would not vary from this average by more than four times the 
probable error. 
2 These December 1 prices were reported by crop reporters and not by the regular price reporters, Who 
report on the 15th of each month. 
3 Average value of entire 1924 crop, per bushel, whether sold or to be sold when the inquiry was made by 
the department in March, 1925. 
* Applies to the straight average: Computed to three decimal places to show the difference from the 
figure for the average given above which is computed to only one decimal place, and from the figure for 
the weighted average below it. 
4 Applies to the weighted average : Computed to three decimal places to show the difference from the 
rounded figure and from the figure for straight average above it. 
Generally speaking, however, the coefficient of variability of wheat 
prices is usually less than 10 per cent. With a sample of only 36 
reports in Maryland for March, 1926, the relative probable error 
of the average was only 0.6 per cent. The probabilities are ninety- 
nine out of one hundred that a much larger sample collected in Mary- 
land in the same way and at the same time would not vary by more 
than 2.4 per cent (four times the relative probable error) from the 
average obtained. In a State like Kansas, with 100 or more reports, 
four times the probable error is 2 per cent or less. The larger num- 
ber of reports as to December 1 prices reduces the probable error of 
the aveage to a point where four times the probable error is only 0.4 
per cent for Kansas and 2 per cent for Maryland. 
The prices or value of the Kansas wheat crop as determined near 
the close of the crop year (in March, 1925), when the reporter was 
asked to estimate the average price for the season, have about twice 
the variability of a monthly price. This greater variability is to 
be expected, as a monthly price is affected by variations in different 
parts of the State on a given date, whereas the season price covers 
variability owing to changes in prices over a period of several 
months. The monthly price might be said to have variability in 
