**Quartiles** are values that split up a dataset into four equal parts.

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

**Q _{i} = L + (C/F) * (iN/4 – M)**

where:

**L**: The lower bound of the interval that contains the i^{th}quartile**C**: The class width**F**: The frequency of the interval that contains the i^{th}quartile**N**: The total frequency**M**: The cumulative frequency leading up to the interval that contains the i^{th}quartile

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

**Example: Calculate Quartiles for Grouped Data**

Suppose we have the following frequency distribution:

Now suppose we’d like to calculate the value at the third quartile (Q_{3}) of this distribution.

The value at the third quartile will be located at position (iN/4) in the distribution.

Thus, (iN/4) = (3*92/4) = 69.

The interval that contains the third quartile will be the **21-25** interval since 69 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 i^{th} quartile

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

**C**: The class width

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

**F**: The frequency of the interval that contains the i^{th} quartile

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

**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 i^{th} quartile

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

We can then plug in all of these values into the formula from earlier to find the value at the third quartile:

- Q
_{i}= L + (C/F) * (iN/4 – M) - Q
_{3}= 21 + (4/12) * ((3)(92)/4 – 58) - Q
_{3}= 24.67

The value at the third quartile is **24.67**.

You can use a similar approach to calculate the values for the first and second quartiles.

**Additional Resources**

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

How to Find Mean & Standard Deviation of Grouped Data

How to Find the Mode of Grouped Data

How to Find the Median of Grouped Data

Grouped vs. Ungrouped Frequency Distributions