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The process for finding the range of grouped data involves first organizing the data into groups or categories. Then, the highest value in each group is identified and recorded. Next, the lowest value in each group is also identified and recorded. Finally, the difference between the highest and lowest values is calculated to determine the range. For example, if the data is grouped into age categories of 0-10, 11-20, 21-30, the range would be calculated by subtracting the lowest age (0) from the highest age (30) to get a range of 30. This process can be applied to any type of grouped data, such as income ranges, test scores, or population demographics.
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 , 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:
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:
Cite this article
stats writer (2024). What is the process for finding the range of grouped data and what are some examples?. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/what-is-the-process-for-finding-the-range-of-grouped-data-and-what-are-some-examples/
stats writer. "What is the process for finding the range of grouped data and what are some examples?." PSYCHOLOGICAL SCALES, 28 Jun. 2024, https://scales.arabpsychology.com/stats/what-is-the-process-for-finding-the-range-of-grouped-data-and-what-are-some-examples/.
stats writer. "What is the process for finding the range of grouped data and what are some examples?." PSYCHOLOGICAL SCALES, 2024. https://scales.arabpsychology.com/stats/what-is-the-process-for-finding-the-range-of-grouped-data-and-what-are-some-examples/.
stats writer (2024) 'What is the process for finding the range of grouped data and what are some examples?', PSYCHOLOGICAL SCALES. Available at: https://scales.arabpsychology.com/stats/what-is-the-process-for-finding-the-range-of-grouped-data-and-what-are-some-examples/.
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