Example:  Find the median of a groued frequency of marks obtained , out of 100,
by 53 students in maths exam.


Marks
No of students(f)
0-10
5
10-20
3
20-30
4
30-40
3
40-50
3
50-60
4
60-70
7
70-80
9
80-90
7
90-100
8


Solution
Find the cumulative frequency of the given data distribution.


Marks
No of students(f)
Cumulative Frequency(cf)
0-10
5
5
10-20
3
8
20-30
4
12
30-40
3
15
40-50
3
18
50-60
4
22
60-70
7
29
70-80
9
38
80-90
7
45
90-100
8
53


In distibution above, n = 53. So, $n/2$ = 26.5

The class whose cumulative frequency is equal or greater than (and nearly equal to) $n/2$ is called median class.

So median class for $26.5$ is $60-70$

Since  Median = $l$ + $({n/2-cf}/{f})$ $×h$

Substituting the value $n/2=26.5$ , $l=60$ $cf$= $22$, $f=7$ $h=10$,
we get,
          Median = $60$ + $({26.5-22}/{7})$ $×10$
				 = $60$ + $45/7$
				 = $66.4$
	
So, about half the student have scored marks less than $66.4$, and other half have scored
marks more than $66.4$