You can use the following formula to calculate percentile rank for grouped data:

**Percentile Rank = L + (RN/100 – M) / F * C**

where:

**L**: The lower bound of the interval that contains the percentile rank**R**: The percentile rank**N**: The total frequency**M**: The cumulative frequency leading up to the interval that contains the percentile rank**F**: The frequency of the interval that contains the percentile rank**C**: The class width

The following example shows how to use this formula in practice.

**Example: Calculate Percentile Rank for Grouped Data**

Suppose we have the following frequency distribution:

Now suppose we’d like to calculate the value at the 64th percentile of this distribution.

The interval that contains the 64th percentile will be the **21-25** interval since 64 is between the cumulative frequencies of 58 and 70.

Knowing this, we can find each of the values necessary to plug into our formula:

**L**: The lower bound of the interval that contains the percentile rank

- The lower bound of the interval is
**21**.

**R**: The percentile rank

- The percentile we’re interested in is
**64**.

**N**: The total frequency

- The total cumulative frequency in the table is
**92**.

**M**: The cumulative frequency leading up to the interval that contains the percentile rank

- The cumulative frequency leading up to the 21-25 class is
**58**.

**F**: The frequency of the interval that contains the percentile rank

- The frequency of the 21-25 class is
**12**.

**C**: The class width

- The class width is calculated as 25 – 21 =
**4**.

We can then plug in all of these values into the formula from earlier to find the value at the 64th percentile:

- Percentile Rank = L + (RN/100 – M) / F * C
- 64th Percentile Rank = 21 + (64*92/100 – 58) / 12 * 4
- Percentile Rank = 21.293

The value at the 64th percentile is **21.293**.

**Additional Resources**

The following tutorials provide additional information for working with grouped data:

How to Find Mean & Standard Deviation of Grouped Data

Grouped vs. Ungrouped Frequency Distributions