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 = Umax – Lmin
where:
- U: Upper limit of maximum interval
- L: Lower limit of minimum interval
Formula 2: Use Midpoints
Range of Grouped Data = Midpointmax – Midpointmin
where:
- Midpointmax : Midpoint of maximum interval
- Midpointmin : 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:
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 = Umax – Lmin
- 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 = Midpointmax – Midpointmin
- 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 = Umax – Lmin
- 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 = Midpointmax – Midpointmin
- 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