Statistical Investigations 403
Some good illustrations of the merit and defect of the ogive-median method may be found in a further paper published in 1907. In "Vox populi1" Galton begins by stating that
"in these democratic days any investigation into the trustworthiness and peculiarities of popular judgments is of interest,"
and proceeds to illustrate the "Vox populi" by discussing the 787 answers given in a weight judging competition at the West of England Annual Fat Stock Show at Plymouth. The judgments turned on what a selected fat ox would weigh after being slaughtered and dressed. Galton considers that the entrance fee of 6d. and the hope of a prize deterred practical joking and that the judgments would be largely those of butchers and farmers experienced in the matter.
"The judgments were unbiased by passion and uninfluenced by oratory and the like.... The average competitor was probably as well fitted for making a just estimate of the dressed weight of the ox, as an average voter is to judge the merits of most political issues on which he votes."
Galton gives the following table of results and the diagram on page 404
Distribution of the estimates of the dressed weight of a particular living ox,
made by 787 different persons.
|
Degrees of the
length of Array
0°-100° |
Estimates
in lbs. |
Gentiles |
Excess of Observed over Normal |
|
Observed deviates
from 1207 lbs. |
Normal
p.e. = 37 |
Francis Galton |
Karl Pearson |
|
0 |
|
|
|
|
|
|
5 |
1074 |
-133 |
- 90 |
+43 |
-'23 |
|
10 |
1109 |
- 98 |
- 70 |
+28 |
-11 |
|
15 |
1126 |
- 81 |
- 57 |
- 24 |
- 9 |
|
20 |
1148 |
- 59 |
- 46 |
+13 |
+ 1 |
|
q, 25 |
1162 |
- 45 |
- 37 |
+ 8 |
+ 5 |
|
30 |
1174 |
- 33 |
- 29 |
+ 4 |
+ 7 |
|
35 |
1181 |
- 26 |
-21 |
+ 5 |
+ 7 |
|
40 |
1188 |
- 19 |
-14 |
+ 5 |
+ 5 |
|
45 |
1197 |
- 10 |
- 7 |
+ 3 |
+ 6 |
|
M 50 |
1207 |
0 |
0 |
0 |
+ 8 |
|
55 |
1214 |
+ 7 |
+ 7 |
0 |
+ 7 |
|
60 |
1219 |
+ 12 |
+14 |
- 2 |
+ 4 |
|
65 |
1225 |
+ 18 |
+21 |
- 3 |
+ 1 |
|
70 |
1230 |
+ 23 |
+29 |
- 6 |
- 2 |
|
q3 75 |
1236 |
+ 29 |
+37 |
- 8 |
- 5 |
|
80 |
1243 |
+ 36 |
+46 |
-10 |
- 8 |
|
85 |
1254 |
+ 47 |
+57 |
-10 |
- 9 |
|
90 |
1267 |
+ 52 |
+70 |
-18 |
-11 |
|
95 |
1293 |
+ 86 |
+90 |
- 4 |
- 8 |
q,, q,i the first and third quartiles, stand at 25° and 75° respectively. m, the median or middlemost value, stands at 50°. The dressed weight proved to be 1198 lbs.
' Nature, Vol. LXXV, pp. 450-51, March 7, 1907.
51-2
