Francis Galton 
389 
distinct tendency in the smaller values to be the more numerous. This seems 
due to the fact that the curve of distribution (see Natural Inheritance) is always 
convex towards its axis ; consequently 6 - c is on the average less than ^ (a — c). 
TABLE II. 
Values of X derived from 300 Lists of Marks in various Civil Service 
Examinations. 
Mean values of successive groups of 
25 cases 
74-4 
74-6 
70-6 
74- 7 
75- 7 
70-9 
70-4 
68-8 
73-5 
73- 5 
74- 7 
731 
50 cases 
74-5 
72- 6 
73- 3 
69-6 
73-5 
73-9 
100 cases 
73-6 
72-9 
73-7 
Mean of all 300 cases, 73-4. 
Subject to this qualification, the Mean is no more than the average of random 
values between certain limits. Those limits are created by the conditions (1) that 
b cannot exceed a though it may be equal to a, in which case one of the limits 
is 100 (a — c) divided by 2 (a — c), or 50 ; (2) that b cannot exceed c though it may 
be equal to c, in which case the other limit is 100 (a — c) divided by (a — c) + 0, 
or 100. 
TABLE III. 
Distribution of 300 Observed Values of X. 
50— 
55— 
60— 
65- 
70— 
75— 
80— 
85— 
90— 
95— 
Total 
40 
36 
27 
31 
32 
23 
34 
30 
26 
21 
300 
76 
58 
55 
64 
47 
-> 
300 
166 
134 
300 
Therefore it appears to be merely a coincidence that calculation and observation 
lead to much the same conclusion. The principle on which the former is based 
