VI.—THE FREQUENCY-DISTRIBUTION, Fas 
distribution of deaf-mutism amongst the offspring of parents one 
of whom at least was a deaf mute. In general less than one-fifth 
of the children are deaf-mutes : at the other end of the range the 
cases in which over 80 per cent. of the children are deaf-mutes are 
nearly three times as many as those in which the percentage lies 
between 60 and 80. The numbers are, however, too small to form 
a very satisfactory illustration. 
REFERENCES. 
(1) Pearson, KARL, “Skew Variation in Homogeneous Material,” Phil. 
Trans. Roy. Soc., Series A, vol. clxxxvi. (1895), pp. 343-414. 
(2) PEARsoN, KARL, ‘“Cloudiness: Note on a Novel Case of Frequency,” 
Proc. Roy. Soe., vol. Ixii, (1897), p. 287. 
(3) PEARSON, KARL, ‘Supplement to a Memoir on Skew Variation,” Phil. 
Trans. Roy. Soc., Series A, vol. exevii. (1901), pp. 443-459. 
(4) PArETO, VILFREDO, Cours d’économie politique ; 2 vols., Lausanne, 1896-7. 
See especially tome ii., livre iii., chap. i., ‘La courbe des revenus.” 
The first three memoirs above are mathematical memoirs on the theory 
of ideal frequency-curves, the first being the fundamental memoir, and 
the second and third supplementary. The elementary student may, 
however, refer tc them with advantage, on account of the large collection 
of frequency-distributions which is given, and from which some of the 
illustrations in the preceding chapter have been cited. Without 
attempting to follow the mathematics, he may also note that each of 
our rough empirical types may be divided info several sub-types, the 
theoretical division into types being made on different grounds. 
The fourth work is cited on account of the author’s discussion of the dis- 
tribution of wealth in a community, to which reference was made in § 15. 
In connection with the remarks in § 6, on the grouping of ages, 
reference may be made to the following in which a different conclusion 
is drawn as to the best grouping : — 
(5) Youne, ALLYN A., “‘ A Discussion of Age Statistics,” Census Bulletin 18, 
Bureau of the Census, Washington, U.S.A., 1904. 
Reference should also be made to the Census of England and Wales, 
1911, vol. vii., *‘ Ages and Condition as to Marriage,” especially the 
Report by Mr George King on the graduation of ages, 
EXERCISES. 
1. If the diagram fig. 6 is redrawn to scales of 300 observations per interval 
to the inch and 4 inches of stature to the inch, what is the scale of observa- 
tions to the square inch ? 
If the scales are 100 observations per interval to the centimetre and 2 inches 
of stature to the centimetre, what is the scale of observations to the 
square centimetre ? 
2. If fig. 10 isredrawn to scales of 25 observations per interval to theinch and 
2 per cent. to the inch, what is the scale of observations to the square inch ? 
If the scales are ten observations per interval to the centimetre and 1 per cent. 
to the centimetre, what is the scale of observations to the square centimetre ? 
3. If a frequency-polygon be drawn to represent the data of Table I., what 
number of observations will the polygon show between death-rates of 165 
and 17'5 per thousand, instead of the true number 159 ? 
4. If a frequency-polygon be drawn to represent the data of Table V., 
what number of observations will the polygon show between head-breadths 
5'95 and 6°05, instead of the true number 236 ? 
1UF