3323 THEORY OF STATISTICS.
rucians, or Table IV., ref. 16, in Appendix I.) gives the values
directly, and these have been utilised for tle following : the
student can estimate the values roughly by a combined use of the
area and ordinate tables for the normal curve given in Chapter
XV., remembering to divide the ordinates given in that table by
J/27 50 as to make the area unity— Value of 3,
Median . . 0-3989423
Deciles 4 and 6 . 03863425
9. oand 7 : v ; 0:3476926
si and 8 : : 0-2799619
sit sliand 9 . . 01754983
Quartiles ; 03177766
Inserting these values of y, in equation (1), we have the
following values for the standard errors of the median, deciles,
etc., and the values given in the second column for their probable
errors (Chap. XV. § 17), which the student may sometimes find
useful :—
Standard error is Probable error is
o/Nn multiplied by o/Nn multiplied by
Median : . 125331 084535
Deciles 4 and 6 . 1-26804 0-85528
ni 9 and THE . 1:31800 0-88897
yw £2 and 3H 1-42877 0:96369
yw Sl and 1-70942 1-15298
Quartiles . 1-36263 0-91908
It will be seen that the influence of fluctuations of sampling on
the several percentiles increases as we depart from the median:
the standard error of the quartiles is nearly one-tenth greater than
that of the median, and the standard error of the first or ninth
deciles more than one-third greater.
5. Consider further the influence of the form of the frequency-
distribution on the standard error of the median, as this is an
important form of average. For a distribution with a given
number of observations and a given standard-deviation the
standard error varies inversely as y,. Hence for a distribution in
which y, is small, for example a U-shaped distribution like that
of fig. 18 or fig. 19, the standard error of the median will be
relatively high, and it will, in so far, be an undesirable form of
average to employ. On the other hand, in the case of a distribu-
tion which has a high peak in the centre, so as to exhibit a value
of y, large compared with the standard-deviation, the standard
error of the median will be relatively low. We can create such a
. LN
