THEORY OF STATISTICS. 
(9) JAcoB, S. M., “On the Correlations of Areas of Matured Crops and the 
Rainfall,” Mem. Asiatic Soc. Bengal, vol. ii., 1910, P- 847. 0(3Y7 
contains remarks on the effects of errors on the correlations and 
regressions, with especial reference to this problem.) 
(10) Brown, W., “Some Experimental Results in Correlation,” Proceedings 
of the Sixth International Congress of Psychology, Geneva, August 1509. 
Correlations between Indices, ete. 
(11) PrArsoN, KARL, ‘On a Form of Spurious Correlation which may arise 
when Indices are used in the Measurement of Organs,” Proc. Loy. Soc., 
vol. Ix., 1897, p. 489. (§§8, 9.) 
(12) GALTON, Francis, ‘Note to the Memoir by Prof. Karl Pearson on 
Spurious Correlation,” 4bid., p. 498. 
(18) YuLg, G. U., “On the Interpretation of Correlations between Indices or 
Ratios,” Jour. Roy. Stat. Soc., vol. Ixxiii., 1910, p. 644. 
(14) Brown, J. W., M. GREENWoOD, and Frances Woop, “A Study of 
Index-Correlations,” Jour. Roy. Stat. Soc., vol. 1xxvii., 1914, pp.317-46. 
The Weighted Mean. 
(15) PEARSON, KARL, ‘‘Note on Reproductive Selection,” Proc. Roy. Soc., 
vol. lix., 1896, p. 301. (Eqn. (15).) 
Standardisation or Correction of Death-rates, etc. 
(16) TaTrAM, JoEN, Supplement to the Fifty-fifth Annual Report of the 
Regisirar-General for England and Wales: Introductory Letters to 
Pt. I. and Pt. 11, Also Supplement to Sixty-fifth Report: Introductory 
Letter to Pt. II. (Cd. 7769, 1895 ; 8503, 1897 ; 2619, 1908). 
(17) NewsHOLME, A., and T. H. O. STEVENSON, ‘‘ The Decline of Human 
Fertility in the United Kingdom and other Countries, as shown by 
Corrected Birth-rates,” Jour. Roy. Stat. Soc., vol. lxix., 1906, p. 34. 
(18) YuLe, G. U., “On the Changes in the Marriage and Birth Rates in 
England and Wales during the past Half Century,” etc., <bid., p. 88. 
(19) Heron, Davi, “The Influence of Defective Physique and Unfavourable 
Home Environment on the Intelligence of School Children,” Eugenics 
Laboratory Memorrs, viii. ; Dulau & Co., London, 1910. 
Miscellaneous. 
(20) PeArsoN, KARL, ALICE LEE, and L. BRAMLEY-MOORE, ‘Genetic 
(reproductive) Selection: Inheritance of Fertility in Man and of 
Fecundity in Thoroughbred Racehorses,” Phil. Trans. Roy. Soc., 
Series A, vol. cxcii., 1899, p. 257. 
(A number of theorems of general application are given in the intro- 
ductory part of this memoir, some of which have been utilised in §§ 12 
13 of the preceding chapter.) 
EXERCISES. 
1. Find the values obtained for the standard-deviations in Examples ii. 
(p. 139) and iii. (p. 141) of Chapter VIII. on applying Sheppard’s correction 
for grouping. : 
2. Show that if a range of six times the standard-deviation covers at least 18 
class-intervals (¢f. Chap. VI. § 5), Sheppard’s correction will make a ditference 
of less than 0°5 per cent. in the rough value of the standard-deviation. 
3. (Data from the decennial supplements to the Annual Reports of the 
Registrar-General for England and Wales.) The following particulars are 
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