24 THEORY OF STATISTICS. 
for which the standard error of the median is exactly equal to 
a/a/n is shown in fig. 53: it will be seen that it is by no means 
a very striking form of distribution; at a hasty glance it might 
almost be taken as normal. In the case of distributions of a form 
more or less similar to that shown, it is evident that we cannot 
at all safely estimate by eye alone the relative standard error of 
the median as compared with o/s/7. 
6. In the case of a grouped frequency-distribution, if the 
number of observations is sufficient to make the class-frequencies 
run fairly smoothly, ¢.e. to enable us to regard the distribution 
Fic. 53. 
as nearly that of a very large sample, the standard error of any 
percentile can be calculated very readily indeed, for we can 
eliminate o from equation (1). Let f, be the frequency-per- 
class-interval at the given percentile—simple interpolation will 
give us the value with quite sufficient accuracy for practical 
purposes, and if the figures run irregularly they may be smoothed. 
Let o be the value of the standard-deviation expressed in class- 
intervals, and let # be the number of observations as before. 
Then since 7, is the ordinate of the frequency-distribution when 
drawn with unit standard-deviation and unit area, we must 
have 
ag 
Yo=—Jp 
Aa,