THEORY OF STATISTICS. 
The Geometric Mean. 
(4) Jevons, W. STANLEY, 4 Serious Fall in the Value of Gold ascertained 
and its Social Effects set forth ; Stanford, London, 1863. Reprinted 
in Investigations in Currency and Finance ; Macmillan, London, 1884. 
(The geometric mean applied to the measurement of price changes. ) 
(5) JEVoNs, W. STANLEY, ‘On the Variation of Prices and the Value of 
the Currency since 1782,” Jour. Roy. Stat. Soc., vol. xxviii., 1865. 
Also reprinted in volume cited above. 
(6) EpcEworrH, F. Y., “On the Method of ascertaining a Change in the 
Value of Gold,” Jour. Roy. Stat. Soc., vol. xlvi., 1883, p. 714. (Some 
a of the reasons assigned by Jevons for the use of the geometric 
mean, 
(7) GALTON, FRANCIS, ‘The Geometric Mean in Vital and Social Statistics,” 
Proc. Roy. Soc., vol. xxix., 1879, p. 365. 
(8) MCALISTER, DoNALD, ‘The Law of the Geometric Mean,” ¢bid., p. 367. 
(The law of frequency to which the use of the geometric mean would 
be appropriate.) 
(9) KarreyN, J. C., Skew Frequency-curves in Biology and Statistics ; 
Noordhoff, Groningen, and Wm. Dawson, London, 1903. (Contains, 
amongst other forms, a generalisation of McAlister’s law.) 
(10) CrawFrorD, G. E., ‘“ An Elementary Proof that the Arithmetic Mean 
of any number of Positive Quantities is greater than the Geometric 
Mean,” Proc. Edin. Math. Soc., vol. xviii., 1899-1900. 
See also refs. 1 and 2. 
The Mode. 
(11) PrArsoN, KARL, ‘‘Skew Variation in Homogeneous Material,” Phil. 
Trans. Roy. Soc., Series A, vol. clxxxvi., 1895, p. 843. (Definition of 
mode, p. 345.) 
(12) YuLg, G. U., ‘“Notes on the History of Pauperism in England and 
Wales, ete. : Supplementary Note on the Determination of the Mode,” 
Jour. Roy. Stat. Soc., vol. lix., 1896, p. 848. (The note deals with 
elementary methods of approximately determining the mode : the one- 
third rule and one other.) 
(18) PEARSON, KARL, ‘On the Modal Value of an Organ or Character,” 
Biometrika, vol. i., 1902, p. 260. (A warning as to the inadequacy of 
mere inspection for determining the mode.) 
Estimates of Population. 
(14) WaArErs, A. C., “A Method for estimating Mean Populations in the 
last Intercensal Period,” Jour. Roy. Stat. Soc., vol. lxiv., 1901, p. 293. 
(15) Warkrs, A. C., Estimates of Population : Supplement to Annual Report of 
the Registrar-General for England and Wales (Cd. 2618, 1907, p. cxvii.) 
For the methods actually used, see the Reports of the Registrar-General 
of England and Wales for 1907, pp. cxxxii-cxxxiv, and for 1910, 
pp. xi-xil. Cf. SNxow, ref. 11, Chap. XII, for a different method 
based on the symptoms of growth such as numbers of births or of houses. 
Index-numbers. 
These were incidentally referred to in § 25. The general theory of 
index-numbers and the different methods in which they may be formed 
are not considered in the present work. The student will find copious 
references to the literature in the following :— 
(16) EpcEWORTH, E. Y., “Reports of the Committee appointed for the 
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