By Student 
15 
Standard deviation of standard deviations 
Calculated -8556 ± -Qlo 
Observed '9066 
Difference = + -0510 
Comparison of Fit. Theoretical Equation : y = - ■ 
Scale in terms 
of standard 
deviation of 
population 
o 
+^ 
0) 
c 
0 
0 
0 
;o 
0 
8^ 
0 
+J 
<£. 
00 
0 
G: 
0 
GO 
•-i 
(J) 
p 
c 
"--I 
0 
>--< 
+s 
■p 
Calculated 
frequency 
u 
10| 
•21 
■4 5 A 
78A 
87 
88 
&u 
71 
58 
45 
33 
23 
15 
95 
7 
Observed 
frequency 
3 
14 
107 
67 
73 
77 
77^ 
64 
m 
49i 
35 
28 
12i 
9 
lli 
7 
Difference 
+u 
+ 4 
-2* 
-8 
+ 42* 
-11}, 
-14 
- 11 
-4 
— 7 
- 53 
+ 4i 
+ 2 
+ 5 
-2A 
_ .1 
+ 6 
0 
whence x^ = 48-06, /'= -000,06 (about). 
In tabling the observed frequency, values between "0125 and 'OSTo were 
included in one group, while between "0875 and '0125 they wei'e divided over the 
two groups. As an instance of the irregularity due to grouping I may mention 
that there were 31 cases of standard deviations 1'30 (in terms of the grouping) 
which is :o\\l in terms of the standard deviation of the population, and they were 
therefore divided over the groups '4 to "5 and "o to '6. Had they all been counted 
in groups "5 to '6 %- would have fallen to 29'85 and P would have risen to 'OS. 
The ')(^ test presupposes random sampling from a frequency following the given 
law, but this we have not got owing to the interference of the grouping. 
When, however, we test the ^'s where the grouping has not had so much effect 
we find a close correspondence between the theory and the actual result. 
There were three cases of infinite values of z which, for the reasons given 
above, were given the next largest values which occurred, namely +6 or — 6. 
The rest were divided into groups of "1 ; "04, '05 and "06, being divided between 
the two groups on either side. 
The calculated value for the standard deviation of the frequency curve was 
1 (+ "017) while the observed was 1039. The value of the standard deviation is 
really infinite, as the fourth moment coefficient is infinite, but as we have arbi- 
trarily limited the infinite cases we may take as an approximation ^j^q fi'<"ii 
which the value of the probable error given above is obtained. The fit of the 
curve is as follows : — 
