230 Variation and Correlation of the Human Skull 
Dealing first with the L^^ normal curve — the general equation y = y^e~^^l'^'^'', 
137 
where ?/o = — and o- = 6-26665, becomes y = S-1-2lQe-''^^'"^'''\ and the origin is at 
o-v27r 
189'06 mm. I will now apply Pearson's test of goodness of fit to the curve*. 
The following table shows the observed frequencies {m,.'), the frequencies calculated 
from the curve (wi^), and the ratio {nir — m/y/nir : 
mm. 
Observed 
Calculated 
{in m '1- 
LJ: ILL 
176 aud under 
2 
3-1 
•39 
177 
4 
1-4 
4-83 
178 
3 
1-8 
■80 
179 
2 
2-4 
•07 
180 
2 
3-1 
•39 
181 
4 
3-8 
•01 
182 
1 
4-6 
2' 82 
183 
2 
5'5 
184 
8 
6-3 
•46 
185 
9 
7-1 
•61 
186 
9 
•22 
187 
9 
8-2 
•08 
188 
11 
8-6 
•67 
189 
8 
8-7 
•06 
190 
10 
8-6 
•23 
191 
8 
8-3 
•01 
192 
8 
7-8 
•005 
193 
8 
7-1 
•11 
194 
1 
6-4 
4^57 
195 
4 
5-6 
•46 
196 
5 
4-7 
•02 
197 
4 
3-9 
■003 
198 
4 
3-1 
•26 
199 
4 
2-5 
•90 
200 
4 
1-9 
2-32 
201 
1 
1-4 
•11 
202 and over 
3-4 
■58 
Totals 
137 
137 
23^12 
Here the number of groups is 27, and ;^^ = 23^12, and turning to Elderton's 
Tablesf we find for ?i' = 27 and = 23, that P = •632947; that is, if our series 
of English skulls obeyed the " normal " frequency distribution for the character L 
the frequency polygon would be more " peaked " in about 63 out of 100 trial 
samples of 137 skulls each. The normal curve, therefore, fits the observations 
quite satisfactorily. 
It is unnecessary to discuss the normal curve for B% in great detail; its 
equation is y = \Vl Q2Qe-'^^^^'=\ with centre at 134-68 mm. In this case x'^^'^^ 
* FUL Mag. Vol. l. pp. 157—175 (July, 1900), and Biometrika, Vol. i. p. 155. 
t Biometrika, Vol. i. p. 101. 
