494 FRETS, THE INDEX CEPHALICUS. 
qı = 77.9, Med = 79.8 and q3= 82.0, for the sisters qj — 78.5. 
Med = 80.5 and q3 = 82.51). 
The distribution of frequency agrees rather well with the 
calculated numbers (tab. 3). For the brothers the divergence 
is large for the index 79 (69 and 85) and for the index 83 (59 and 
43). In both cases three times the standard error of sampling 
3 vi) is still larger. With the whole material the index 
of the men is 81.04 — 80.4 — 0.64 lower than of the women and 
with the brothers and sisters this difference is 81.12 — 80.59 = 0 53. 
The standarddeviation of the index of the brothers is a little 
larger than of the men. 
According to an investigation of K. PEARSON (1897) on the varia- 
bility of man and woman there would be no distinct difference 
between the variabilty of both. For the headindex it is evident — 
as far as the material of this investigation goes — that the index 
of man is somewhat smaller than of woman and that the varia- 
bility of the index of man is surely somewhat larger than of 
woman (see p. 492). 
The mean headlength and headbreadth in my material has been 
calculated for 933 adult men and for 1426 adult women (tab. 
4 — 7).2) As adults I have taken all that are 20 years of age and older. 
1) A year before we found for 610 brothers and 610 sisters 
M) +>, = 80.56 + 3.25 and M, + c.,— 81.09 + 2.995 
2) I omit the publication of the tables 4 and 5, where headiengths and 
headbreadths are given in mM. The distribution of frequency of these tables 
is irregular. The reason is that the observations are done in mM. exact, 
but that I have often rounded them off. I did so, because the division of 
my compasses is per 5 mM. and the division per 1 mM. has been supplied 
by myself as exactly as possible. Several times a little above 19 I shall have 
noted as 19 and not as 19.1. Something above 19.1 I shall often have noted 
as 19.2 So there are too few observations of 19.1 cM. The same is true 
for 19.4, 19.9 etc. To eliminate this mistake I have grouped in tab. 6 the frequen- 
cy according toa scale of 2.5 mM. (in tab. 4 and Stoascale of 5 mM., also). 
It has to be mentioned that in the diagrams 5—8 the mean is drawn in 
the normal curve a little to the left. The mean of the normal curve is a 
little smaller. The reason is that the original mean has been calculated from 
the material that is grouped in class-intervals of 1 mM. Grouping the material 
in class-intervals of 2.5 mM. in the way that we applicated the mean is 
somewhat too small. 
