42 KANSAS CITY REVIEW OF SCIENCE. 
ness, while a greater number would be ranked about average. The shallow curve 
of the bad marksman is suggested. The two cases are, however, not exactly 
alike, for a good shot is one which lies nearest to the mark, while the virtue of an 
act is judged by a higher standard than the supposed mark. Hence the marksman 
would always aim at the mark, while the man who wishes to be as good as other 
people, usually tries to make sure of having enough of good deeds by putting in 
a few extra good ones toward the last—that is, he changes his aim somewhat in 
order to polish up his curve into satisfactory shape. 
That this same law of probability applies to the distribution of mental ability 
in a mass of people is well known. Comparatively few people are brilliant and 
comparatively few are stupid (the opportunities being supposed equal). The great 
majority of people rank near the average. Among others, Professor Hinrichs has 
investigated this subject, by a comparison of class markings at the State Univer- 
sity of lowa. The results here given are from the markings of the Freshman class 
“in Physics. 
The results are obtained by combining independent markings for recita- 
tion, notes on lectures, and laboratory work, as determined by three differ- 
ent instructors. The greatest pains were taken to secure just markings, the valu- 
ations being repeated several times. ‘The best students were marked 100, and 
below 65 was counted a failure 
In the following table the numbers are grouped in fives, go per cent. including 
88 to 92, inclusive, etc. 
The total number of students in the class was 287, and the results agree as 
closely with the theoretical values as would those obtained by making 287 draws 
from an urn containing black and white balls in equal number : 
Standing Piro] ise go 84) 78| 72| 66] 60/Total. 
Number of Students SG sie Se7 80 INS OMY <3 3\287 
NOs penToo fj a | 4.5) 18.5 19.9 28.0 15.7 8.4) 4.2| 1.0|100 
This shows that the chances that the standing of a student will fall in the 
group marked 84, is 80-287 or 28-100, or a little less than one-third. This is the 
grade of the average student, and here the greater number are ranked. For higher 
or lower markings, the number of students is less, the fewest numbers being at 
the extremes of excellence. It will be observed that in this case the numbers are 
not quite the same for grades equally removed from 80 per cent., the probability 
being somewhat in favor of the higher markings. This might possibly be differ 
ent if a greater number of cases were examined. Tt is also to be remembered that 
such students are a selected class of society, and if all of the young people of a 
state were to be thus examined, the grade would probably be somewhat lower, 
and the numbers would perhaps show a more symmetrical arrangement. 
We have previously discussed the mental divergence of men from the norma 
or average man. As might be expected, the same law holds in regard to physi- 
cal dimensions, as was first shown by Quetelet. 
