16 The Probable Error of a Mean 
.2 
Cotiiparisoii of Fit. Theurettcal Equatiun: i/ = -cos^d, z — tan 6. 
) 
1 
•f^ 
1 
1 
)^ 
1 
1 
1 
U-5 
+ 
>^ 
4- 
>-'5 
1^ 
4- 
0 
+ 
§ 
+ 
+ 
Scale of i 
S 
m 
0) 
o 
c> 
So 
1 
o 
CI 
©! 
1 
o 
1 
o 
+3 
? 
1 
1 
o 
1 
1 
o 
+ 
1.-5 
+ 
4- 
+^ 
10 
+ 
0 
-^^ 
l-O 
' — I 
+ 
+ 
3 
Si 
0 
a 1 
Calculated 
frequency 
Observed 
5 
34i 
119 
141 
119 
78| 
44i 
34* 
13i 
5 
frequency 
9 
lU 
33 
43* 
70i 
luH 
15U 
122 
67* 
49 
26^ 
16 
10 
6 
Difference 
+ 4 
+ 5 
-2 
-H 
-1 
-8 
+ 104 
+ 3 
-Jl 
+ 4i 
-8 
+ 2* 
+ 5 
+ 1 
whence 12-44, P=-56. 
This is very satisfactory, especially when we consider that as a rule observa- 
tions are tested against curves fitted from the mean and one or more other 
moments of the observations, so that considerable correspondence is only to be 
expected ; while this curve is exposed to the full errors of random sampling, its 
constants having been calculated quite apart from the observations. 
Diagram III. Comparison of Calculated Standard Deviation Frequency Curve with 750 actual 
Standard Deviations. 
lOOi — I — I — I \ — I \ — I — I \ — I — 1 — I — I — I — 1 1 — \ — 1 — I — \ — I — 1 1 — I — I — 
•1 -2 -3 -4 -5 -fi -7 -8 -9 1-^ 1-1 v? 1-3 1-4 l-"^ 1-7 1-8 1-9 2-0 2-1 2-2 2-3 2-4 2-5 
Scale of Standard Deviation of the Population 
The left middle finger samples show much the same features as those of the 
height, but as the grouping is not so large compared to the variability the curves 
fit the observations more closely. Diagrams III.* and IV. give the standard devia- 
tions and the s's for this set of samples. The results are as follows : — 
* There are three small mistakes in plotting the observed values in Diagram III., which make the fit 
appear worse than it really is. 
