How to Find the Range of Grouped Data (With Examples)


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

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