XVIL—SIMPLER CASES OF SAMPLING FOR VARIABLES. 341
But this gives at once for the standard error expressed in terms
of the class-interval as unit
n,
ym 22 (2)
As an example in which we can compare the results given by
the two different formule (1) and (2), take the distribution of
stature used as an illustration in Chaps. VII. and VIIL and in
$$ 13, 14 of Chap. XV. The number of observations is 8585,
and the standard-deviation 2:57 in., the distribution being
approximately normal : o/,/n=0027737, and, multiplying by the
factor 1-253 . . . . given in the table in § 4, this gives 00348
as the standard error of the median, on the assumption of
normality of the distribution. Using the direct method of
equation (2), we find the median to be 67:47 (Chap. VII. § 15),
which is very nearly at the centre of the interval with a
frequency 1329. Taking this as being, with sufficient accuracy
for our present purpose, the frequency per interval at the median,
the standard error is
J8585
1399 =00349.
As we should expect, the value is practically the same as that
obtained from the value of the standard-deviation on the assumption
 of normality.
Let us find the standard error of the first and ninth deciles
as another illustration. On the assumption that the distribution
 is normal, these standard errors are the same, and equal to
0:027737 x 1'70942=00474. Using the direct method, we
find by simple interpolation the approximate frequencies per
interval at the first and ninth deciles respectively to be 590 and
570, giving standard errors of 00471 and 00488, mean 0-0479,
slightly in excess of that found on the assumption that the frequency
 is given by the normal curve. The student should notice
that the class-interval is, in this case, identical with the unit of
measurement, and consequently the answer given by equation (2)
does not require to be multiplied by the magnitude of the
interval.
In the case of the distribution of panperism (Chap. VIL,
Example i.), the fact that the class-interval is not a unit must
be remembered. The frequency at the median (3-195 per cent.)
is approximately 96, and this gives for the standard error of the
median by (2) (the number of observations being 632) 0:1309
intervals, that is 0:0655 per cent.
7. In finding the standard error of the difference between two