What is the Range of Grouped Data?

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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 , 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_max : Midpoint of maximum interval
• Midpoint_min : Midpoint of minimum interval

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:

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.

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

How to Find the Variance of Grouped Data