490 FRETS, THE INDEX CEPHALICUS. 
Curve 3 for the whole number of women has a somewhat- 
- 
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Diagram 3. 2057 Women. 
Observations. 
Reet WO Normal Curve. 
higher top than the normal 
curve. For the rest we find 
the same properties as with 
curve | and 2. There is a great 
resemblance of the quartiles of 
GALTON for the calculated and 
the observed figures (tab. 1). 
For no index the difference 
between actual and normal 
distribution exceeds the ad- 
mitted fluctuation of sampling. 
Skewness is slight, the mode 
being 80, the mean 81.04. 
The methods applied to my 
material I have also used for 
the known Swedish material 
of Retzius and First (1902). 
Table 2 (p. 488) and diagram 
4 give the results. I found 
the mean, M = 76.122 (RET- 
zius and First give M = 
75.855) and the standard devi- 
ation ¢ + 3.082. For GALTON’S 
quartiles I found qy = 73.5, 
Med = 75.5 and qg == 77.6. 
Curve 4 does not differ 
apparently from the curves 
1—3; but comparing the diffe- 
rences of the actual and the 
normal distribution with the 
standard error of sampling we find in many cases the differences 
too large. The number of observations of the indices 68 — 71 is much 
too small (see tab. 2) and for the indices 73, 74 and 75 much too 
large. Again, for the indices 79 and 80 the figure of observations is 
much too small and beginning with index 84 the number of observati- 
ons is much too large. So there are in this very large material of 44941 _ 
persons great differences between actual and normal distribution. 
