Often we may want to calculate the median of data that is grouped in some way.

Recall that the median represents the value that lies directly in the middle of a dataset, when all of the values are arranged from smallest to largest.

For example, suppose we have the following grouped data:

While it’s not possible to calculate the exact median since we don’t know the raw data values, it is possible to estimate the median using the following formula:

**Median of Grouped Data = L + W[(N/2 – C) / F]**

where:

**L**: Lower limit of median class**W**: Width of median class**N**: Total Frequency**C**: Cumulative frequency up to median class**F**: Frequency of median class

**Note**: The **median class** is the class that contains the value located at N/2. In the example above, there are N = 23 total values. Thus, the median value is the one in position 23/2 = 11.5, which would be located in the class 21-30.

The following examples show how to calculate the median of grouped data in different scenarios.

**Example 1: Calculate the Median of Grouped Data**

Suppose we have the following frequency distribution that shows the exam scored receive by 40 students in a certain class:

In this example, there are N = 40 total values. Thus, the median value lies in the class where 40/2 = 20 is located. The 20th largest value would be located in the **71-80** class.

Knowing this, we can calculate the following values:

**L**: Lower limit of median class:**71****W**: Width of median class:**9****N**: Total Frequency:**40****C**: Cumulative frequency up to median class:**12****F**: Frequency of median class:**15**

We can plug these values into the formula to calculate the median of the distribution:

- Median = L + W[(N/2 – C) / F]
- Median = 71 + 9[(40/2 – 12) / 15]
- Median =
**75.8**

We estimate that the median exam score is **75.8**.

**Example 2: Calculate the Median of Grouped Data**

Suppose we have the following frequency distribution that shows the number of points scored per game by 60 basketball players:

In this example, there are N = 60 total values. Thus, the median value lies in the class where 60/2 = 30 is located. The 30th largest value would be located in the **11-20** class.

Knowing this, we can calculate the following values:

**L**: Lower limit of median class:**11****W**: Width of median class:**9****N**: Total Frequency:**60****C**: Cumulative frequency up to median class:**8****F**: Frequency of median class:**25**

We can plug these values into the formula to calculate the median of the distribution:

- Median = L + W[(N/2 – C) / F]
- Median = 11 + 9[(60/2 – 8) / 25]
- Median =
**18.92**

We estimate that the median exam score is **18.92**.

**Additional Resources**

The following tutorials explain how to perform other common operations with grouped data:

How to Find Mean & Standard Deviation of Grouped Data

How to Find the Mode of Grouped Data

How to Calculate Percentile Rank for Grouped Data