FRETS, THE INDEX CEPHALICUS. 487 
If the divergence of the observed from the theoretical frequency 
exceeds some three times the standard error, the divergence is 
unlikely to have occurred as a mere fluctuation of sampling (YULE). 
Also for this problem PEARSON (1900; ’01) has given complicated 
formulae (p. 491.) 
For the largest differences between actual and normal frequency 
I have calculated the standard error of sampling, so for the indices 
72, 75, 78, 83, 84, 91 and 92. Only for the index 91 three times 
the standard error is larger than this difference. The too large 
number of very high indices is caused by the children with very 
high indices in fam. 3 (tab. C fam. 3k and Tab. E fam. 3e and 38). 
There is little skew- 









ness in the curve; the ss tn me ll 
mode being 80 (81) and "4 [TT SR SI NÉE i | | = 
the means 80.75. iel Eh “ a an 
saa + ++ 4 ; a 
When we look for the À 
Ho, 
hele 1 

total number of menat 
the distribution of indi- 
ces (diagram 2 and tab. ol} A DS DEE 

































































| Hi D Ne 
1), it appears that the „all HA mers | 
top of curve 2 is stilla wl aen ren 
EEH 
little larger than ofcurve vw | | H 
‘ Er ma E 
I. Here too there are +}; El à PEYRE 
toofew dolichocephalics * dele ei EE D is 
(up to index 77) and too # mm } CI | | | 
few brachycephalics PQ aS IL it 
with the index 82—85. 1 71 ie ‘ 1e 
The agreement between a ; | Aa ee 
Ot / + JAN LA ee JE 
actual and normal dis- = mm: / | : aa i 
tribution is good. For a = LED EE 
of nn ah 
index 83 three times rey er er + 
sb Of de do zo À qo D de ds it is un Le ds di ps de dp ob sh ofa 
the standard error is 
still equal to the diffe- Diagram 2. 1545 Men. 
rence between the ob- Observations. 
served and the calcu- 
lated number. The quartiles of GALTON for the normal distribution 
of men differ a little more from the actual distribution than for 
men and women (tab. 1.) 
er Normal Curve. 
