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 assump- 
tion of normality. 
Let us find the standard error of the first and ninth deciles 
as another illustration. On the assumption that the distribu- 
tion 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 fre- 
quency 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