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Finding the Median of Grouped Data

To find the median of arrayed (grouped) data we need to follow the following steps:

Step I: Arrange the grouped data in ascending or descending order, and form a frequency table.

Step II: Prepare a cumulative-frequency table of the data.

Step III: Select the cumulative frequency that is just greater than N2, where N is the total number of observations (variates). Then find the median as follows.

The variate whose cumulative frequency is the selected cumulative frequency, is the median of the data.

If N2 is equal to the cumulative frequency of a variate then

median = mean of this variate and the variate just greater than it.

Solved Examples on Find the Median of Grouped Data /Arrayed Data:

1. Find the median of the following distribution.


Variate

2

5

6

8

10

Number of Students

3

2

5

4

2


Solution:

Here, the frequency distribution is given.

The cumulative-frequency table of the distribution is

Variates

2

5

6

8

10

Frequency

3

2

5

4

                  2       

N = 16

Cumulative Frequency

3

5

10

14

16

Finding the Median of Grouped Data

Here, N2 = 162 = 8.

The cumulative frequency just greater than 8 is 10.

The variate whose cumulative frequency is 10 is 6.

Therefore, the median = 6.


2. Find the median of the arrayed data given below.

10, 11, 11, 12, 12, 12, 13, 14, 14, 15, 15, 15, 15, 16, 16, 17, 18, 19, 19, 20.

Solution:

Putting the data in a frequency table, we have the cumulative frequencies as below.

Problems on Median of Grouped Data

Here, the total frequency N = 20.

So, N2 = 202 = 10.

The cumulative frequency just greater than 10 is 13 and the corresponding variates is 15. So, the median = 15.






9th Grade Math

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