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 \(\frac{N}{2}\), 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 \(\frac{N}{2}\) 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

2 5 6 8 10 |
3 2 5 4 N = 16 |
3 5 10 14 16 |

Here, \(\frac{N}{2}\) = \(\frac{16}{2}\) = 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.

Here, the total frequency N = 20.

So, \(\frac{N}{2}\) = \(\frac{20}{2}\) = 10.

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

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