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th
Corresponding value of 17 observation of cumulative frequency in xi is 28. Hence the
median is 28.

Example-2:Obtain the median for the following frequency distribution.
X 1 2 3 4 5 6 7 8 9
Y 8 10 11 16 20 25 15 9 6
Here the given data is in ascending order of xi.
Cumulative frequency table for the given data is
Xi fi c.f
1 8 8
2 10 18
3 11 29
4 16 45
5 20 65
6 25 90
7 15 105
8 9 114
9 6 120

Here n=120(even).There are two middle numbers in these observations.
 1   N th  N  th
Median==   x Value of [      1 ]observations
 2   2   2 

 1   120 th  120  th  1 
th
th
=   x [      1 ]observations=  x (60 observation + 61 observation)
 2   2   2   2 
 1 
th
th
=  x (5 +5)=5 (Both 60 and 61 observations lie in the cumulative frequency 65 and
 2 
its corresponding value of xi is 5.
Median = 5

Median for Grouped Data
In a grouped data, we may not find the middle observation by looking at the cumulative
frequencies, we have to find out median class.

Median class: if no of observation= N.Location of class whose cumulative frequency is
 N 
a greater than(and nearest to)   and this class is called median class.
 2 
The formula for calculating the Median

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