FRETS, THE INDEX CEPHALICUS. 485 
is with men (¢ = 3.22) larger than with women (¢ = 2.994). 
In agreement with the difference in the arithmetic mean of the 
headindex of men and women we find that according to the 
calculations of the quartiles of GALTON (tab. 1) with one fourth 
of the number of men the headindex is smaller than 77.7, with 
one fourth of the number of women smaller than 78.5. So, among 
the low indices there are more men than women. In the same 
way we find that with three fourths of the number of men the 
index is smaller than 81.8 and with three fourth of the number 
of women smaller than 82.4. 1) Consequently there are among the 
high indices more women than men. The central half of the men 
lies between 81.8 and 77.7 with a range of 4.1; so the Quartile 
82.4 — 785 
2 
= 1.95. Also according to this calculation the variability of the 
index is larger with man than with woman. 
GALTON’S Qj, i.e. the range of ‘variability from g, to Med (qo), 
is for men 79.8 — 77.7 =-2.1, Oc =0 and Q3= 81.8 —.79.8 = 2. 
For women Q, = 80.4— 78.5 — 1.9 and Qs: = 82.4 — 80.4=2. 
Thus the variations are grouped fairly regularly around the 
Mediane. 
Whether the variability is regular, has further. been examined in 
making curves of frequency, where the distribution of the indices 
in the material is compared with the normal distribution. On the 
question, what formels are to be used in investigations of this kind, 
exists an extensive literature. The conclusion is that for normalising 
a, series of observations on bodylength, headmeasures, skullindices, 
etc, the formel of the normal curve may be used. To this agree 
PEARSON (1896, p. 389, 1897 p. 256), Fawcett (1902), MACDONELL 
(1901), Yure (1912), RANKE (1904). The coefficients of the binomium 
of NEWTON are made use of in different ways for the comparison 
with the distribution of a given material. Very simple, although 
according to PEARSON not scientifical (1896, p 381) is the method 
of QuETELET (1845, p. 124—132) with which I got also good results. 
Further I used ‘the methods of JOHANNSEN (1913, p. 73) and ot 
YULE (1912, p. 307); I give here the results according to YULE. 
(Q) of GALTON is 2.05. Of the women we find Q = 

1) See note page 484. 
