- THEORY OF STATISTICS.
(85) BowLEy, A. L., ‘‘Relations between the Accuracy of an Average and
that of its Constituent Parts,” Jour. Roy. Stat. Soc., vol. 1x., 1897,
p- 855.
(36) BowLey, A. L., “The Measurement of the Accuracy of an Average,”
Jour. Roy. Stat. Soc., vol. 1xxv., 1911, p. 77.
EXERCISES.
1. For the data in the last column of Table IX., Chap. VI. p. 95, find
the standard error of the median (154°7 lbs. ).
9. For the same distribution, find the standard errors of the two quartiles
(142°5 lbs., 168-4 1bs.).
3. For the same distribution, find the standard error of the semi-interquartile
 range.
4. The standard-deviation of the same distribution is 213 lbs. Find the
standard error of the mean, and compare its magnitude with that of the
standard error of the median (Qn. 1).
5. Work out the standard error of the standard deviation for the distribution
 of statures used as an illustration in § 6. (Standard-deviation 2°57 in. ;
8585 observations.) Compare the ratio of standard error of standarddeviation
 to the standard deviation, with the ratio of the standard error of
the semi-interquartile range to the semi-interquartile range, assuming the
distribution normal.
6. Calculate a small table giving the standard errors of the correlation
coefficient, based on (1) 100, (2) 1000 observations, for values of r=0, 0:2, 0°4,
06. 0°8. assuming the distribution normal.

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