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

Recall that the **range** represents the difference between the largest and smallest value in a dataset.

For example, suppose we have the following grouped data:

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

**Formula 1: Use Upper and Lower Limits**

**Range of Grouped Data = U _{max} – L_{min}**

where:

**U**: Upper limit of maximum interval**L**: Lower limit of minimum interval

**Formula 2: Use Midpoints**

**Range of Grouped Data = Midpoint _{max} – Midpoint_{min}**

where:

**Midpoint**: Midpoint of maximum interval_{max}**Midpoint**: Midpoint of minimum interval_{min}

The following examples show how to use each formula in practice.

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

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

Here is how to calculate the range of this grouped data using each formula:

**Formula 1: Use Upper and Lower Limits**

- Range of Grouped Data = U
_{max}– L_{min} - Range of Grouped Data = 100 – 51
- Range of Grouped Data = 49

Using this formula, we estimate that the range is **49**.

**Formula 2: Use Midpoints**

- Range of Grouped Data = Midpoint
_{max}– Midpoint_{min} - Range of Grouped Data = (100+91)/2 – (60+51)/2
- Range of Grouped Data = 95.5 – 55.5
- Range of Grouped Data = 40

Using this formula, we estimate that the range is **40**.

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

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

Here is how to calculate the range of this grouped data using each formula:

**Formula 1: Use Upper and Lower Limits**

- Range of Grouped Data = U
_{max}– L_{min} - Range of Grouped Data = 50 – 1
- Range of Grouped Data = 49

Using this formula, we estimate that the range is **49**.

**Formula 2: Use Midpoints**

- Range of Grouped Data = Midpoint
_{max}– Midpoint_{min} - Range of Grouped Data = (50+41)/2 – (1+10)/2
- Range of Grouped Data = 45.5 – 5.5
- Range of Grouped Data = 40

Using this formula, we estimate that the range is **40**.

**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 Median of Grouped Data

How to Find the Variance of Grouped Data

How to Calculate Percentile Rank for Grouped Data