168 
Tables for Testing Curve Fitting 
Illustration of use of Tables. 
In the table below we have the distribution of the cephalic index in 900 
skulls of modern Bavarian peasants. The frequency is given in the second 
column. In the third column we have the distribution as indicated by the normal 
curve of errors. Is this a reasonable description of the series of measurements ? 
In the fourth column are given the values of — m/ and in the fifth those of 
(m^ — OT/)7)"r- The resulting value of is 18-36 and n' = 24. Table I. gives us: 
n' = U, P = -757489, and %==19, P= -701224. Hence the required 
probability is nearly 737, or roughly in every three cases out of four a random 
sampling would lead to a system of deviations diverging more widely from theory. 
Thus the fit may be considered a good one. 
Cephalic Index of Bavarian Skulls. 
Index 
Observed 
Calculated* 
Under 71-5 
2 
1 
- 1 
1 
72 
0 
1 
+ 1 
1 
73 
2-5 
1-5 
- 1 
•67 
74 
1-5 
3-5 
+ 2 
1-14 
75 
3-5 
7-5 
+ 4 
213 
76 
12-5 
13-5 
+ 1 
•07 
77 
17 
23 
+ 6 
1-57 
78 
37 
35-5 
- 1-5 
•06 
79 
55 
52-5 
- 2-5 
•12 
80 
71-5 
69-5 
- 2 
•06 
81 
82 
86 
+ 4 
-19 
82 
116 
98-5 
-17-5 
3-11 
83 
98 
103 
+ 5 
-24 
84 
107 
99-5 
- 7-5 
•57 
85 
82 
88-5 
+ 6-5 
•48 
86 
74 
72 
- 2 
•06 
87 
58 
54 
- 4 
•30 
88 
34-5 
37-5 
+ 3 
-24 
89 
19 
23-5 
+ 4-5 
•86 
90 
10 
14 
+ 4 
1^14 
91 
8 
7-5 
- 0-5 
•03 
92 
3 
3-5 
+ 0-5 
-07 
93 
1-5 
2 
+ 0-5 
•125 
Over 93-5 
4-5 
2 
- 2-5 
3-125 
Totals 
900 
900 
0 
18-36 
* The calculated values are given to the nearest half skull because the observed values only run to 
this unit. 
t The numbers in the fifth column were obtained from the squares of those in the fourth by dividing 
them by the corresponding numbers in the third. The squaring is at once done from Barloiv's Tables 
and the division to the accuracy required by Crelle's Rechentafeln. Both these books are indispensable 
to biometricians. 
