HOW TO FIND MEDIAN FOR GROUPED DATA

How to find median for grouped data ?

Here we are going to see how to find meadian for grouped data.

Cumulative frequency :

Cumulative frequency of a class is nothing but the total frequency upto that class.

The following examples will illustrate finding meadian for grouped data.

Example 1 :

Find the median for marks of 50 students.

Solution :

Here, the total frequency, N = ∑f = 50

N/2  =  50 / 2  =  25

The median is (N/2)^th value = 25th value.

Now, 25^th value occurs in the cumulative frequency 35, whose corresponding marks is 58.

Hence, the median = 58.

Example 2 :

Find the median for the following data:

Solution :

Here, the total frequency, N = ∑f = 50

N/2  =  50 / 2  =  25

The median is (N/2)^th value = 25th value.

Now, 25^th value occurs in the cumulative frequency 25, whose corresponding marks is 3.

Hence, the median = 3.

Example 3 :

The height (in cm) of 50 students in a particular class are given below:

Find the meadian.

Solution :

Here, the total frequency, N = ∑f = 50

N/2  =  50 / 2  =  25

The median is (N/2)^th value = 25th value.

Now, 25^th value occurs in the cumulative frequency 28, whose corresponding marks is 153.

Hence, the median = 153.

Example 4 :

The hearts of 60 patients were examined through X-ray and the observations obtained are given below:

Find the meadian.

Solution :

Here, the total frequency, N = ∑f = 60

N/2  =  60 / 2  =  30

The median is (N/2)^th value = 30^th value.

Now, 30^th value occurs in the cumulative frequency 31, whose corresponding diameter of heart is 132.

Hence, the median = 132.

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