486 FRETS, THE INDEX CEPHALICUS. 
From diagram 1 it appears that the actual distribution of the indi- 
ree BE ces rather well agrees 
El with the normal distribu- 








Kant tion. The number of ob- 



served very low indices 
ie (up to 70) is somewhat 
too large (curve 1 and 
EEE Gatton’s totals table 
In 11); the number of ob- 
served cases up to the 
index 77 is a little too 























1 H small. So there are too 
| ra | 90 — 

few dolichocephalics. 
- For the indices 78—82 
- the figure of observations 
EE exceeds the calculated 
one; for the indices 83 — 
dt 87 it is smaller. And 
[TTT finally there are too 




















many very high indices. : 
The quartiles of GALTON 





































comma for actual and normal 
TT KIT distribution differ very 
PEER EE | 
their little (table 1). 
Comparising the ac- 
Diagram 1. 3604 Men and Women. tual with the normal dis- 
Observations. tribution the question 
RT en ae arises, whether all the 
observed differences between actual and calculated frequencies 
may have arisen merely as fluctuations of sampling, so that 
the actual distribution may be regarded as strictly normal. I 
have restricted myself to compare the divergences of actual 
from calculated frequencies with fluctuations of sampling in 
the case of single class- intervals. Here YULE gives the formula 
V f(N—f) where f is the expected frequency in a certain interval. 

1) In table 1 a line has been put in the columns of GALTON’s totals 
at the place where the relation between the calculated and the observed 
number changes. 
