24 
The Probable Error of a Mean 
"and tlic quality of the resulting barley is inferior though the yield may be 
greater." 
1900 
Averase 
Standard \ 
Deviation ) 
Standard 1 
Deviation > 
lbs. head corn per acre 
N. K. D. 
K. D. 
Dilf. 
1903 
1935 
1910 
2496 
2108 
1961 
2060 
1444 
1612 
1316 
1511 
2009 
1915 
2011 
2463 
2180 
1925 
2122 
1482 
1542 
1443 
1535 
+ 106 
- 20 
+ 101 
- 33 
+ 72 
- 36 
+ 62 
+ 38 
- 70 
+ 127 
+ 24 
1841-5 
1875-2 
+ 33-7 
63 1 
22-3 
Price of head corn in 
sliillings per quarter 
N. K. D. 
26i 
28' 
29i 
30 
27i 
26" 
29 
29^ 
28i 
30" 
28i 
K. D. 
Diff. 
261- 
261 
281 
29' 
27 
26 
26 
281 
28' 
29 
28 
28-45 27-55 
0 
-11 
r 
1 
6 
3 
■ 1 
. 1 
-i 
. 1 
- -91 
-79 
•28 
cwts. straw per acre 
N. K. D. K. D. 
19i 
22i 
23 
23 
221 
19| 
241 
151 
18' 
IJ] 
17 
19-95 
25 
24 
24 
28 
221 
19i 
22| 
16 
Diff. 
+ 5| 
+ U 
+ 1 
+ 5 
0 
1 
4 
;? 
21-05 +1-10 
2-25 
•80 
Value of crop per acre 
in shillings * 
N. K. D. 
K. D. 
140^ 
152| 
158^ 
204| 
162" 
142 
168 
118 
128^ 
109J 
120 
152 
145 
161 
! 1991 
164" 
1391 
155" 
1171 
121 
116^ 
120i 
145-82 
144-68 
Diff. 
11 J 
71' 
21 
5' 
2 
2\ 
13 
1 
2 
71 
7" 
+ 1-14 
6-67 
2-40 
* Straw being valued at 15.s. per ton. 
In this case I propose to use the approximation given by the normal curve 
and therefore use Sheppard's tables, looking up 
with standard deviation 
V(« - 3) 
the difference divided by — . The probability in the case of yield of corn per 
V o 
33-7 
acre is given by looking up ^ =1'.")1 in Sheppard's tables. This gives = '934, 
or the odds are about 14:1 that kiln-dried corn gives the higher yield. 
•91 
Similarly ^ = 3'25, corresponding to 2> = '9994i,* so that the odds are very 
great that kiln-dried seed gives barley of a worse quality than seed which has not 
been kiln-dried. 
Similarly it is about 11 to 1 that kiln-dried seed gives more sti-aw and about 
2 : 1 that the total value of the crop is less with kiln-dried seed. 
'■■ As pointed out in Section V. the normal curve gives too large a value for [> when the probability 
is large. I find the true value in this case to be /> = -9976. It matters little however to a conclusion of 
this kind whether the odds in its favour are 1,660 : 1 or merely 416 : 1. 
