Median is the value of that item in a distribution which divides it into two equal parts such that the values of one part exceed it and the values of the other are less than this value. In case of frequency distributions, median is the value of the variation under the frequency curve that divides the area under the curve into two equal parts.
We must construct a cumulative frequency distribution to calculate the median for grouped data. Arrange the data in ascending or descending order of the size. Denote the values as X and frequency with f. prepare the cumulative frequency. Apply the formula: Median size of (n + 1)/ 2nd item, and locate the item in the cumulative frequency column.
Procedure to Solve Median for Grouped Data are as follows:
(i) First arrange the data in ascending or descending order.
(ii) After arranging the data, obtain the Cumulative Frequency (C.F) by frequency of the values
(iii) After cumulative frequency table is prepared, we apply the following formula to calculate the median for grouped data
i.e. (n + 1)/2
Where, n = Total number of frequency.
(iv) Then locate the item in the cumulative frequency column.
Example on Median for Grouped Data are as follows:
Example:  Calculate the median of the following data
Income($) 
400 
360 
300 
500 
700 
860 
No. of persons 
17 
15 
9 
40 
50 
12 
Solution: We first arrange the data in ascending order.
Income arranged in ascending order ($) 
No. of persons 

x 
f 
c.f. 
300 
9 
9 
360 
15 
24 
400 
17 
41 
500 
40 
81 
700 
50 
131 
860 
12 
143 

n = 143 

Median for grouped data = size of (n + 1)/ 2nd item, n= 143
Median = size of (143 + 1) / 2nd^{ }item = size of 72^{nd} item.
Let us now examine the CF at each successive value in this manner:
CF = 9 is less than 72
Similarly CF = 24 and CF = 41 are less than 72
But CF = 81 is more than 72 against which x is 500. This is the value of the median. Hence median income = $ 500.