1134 LearnersLast updated on June 18th, 2025
Range in Statistics
The range is the difference between the highest and lowest values of a given data set. The range helps us in understanding the spread of a data. Range is a measure of dispersion. In this topic, we will learn more about range, its formulas, how to calculate, and so on.
What is Range?
In statistical concepts, range is used to understand the spread of data. It is calculated by subtracting the lower value from the upper value in a dataset. It helps get an insight into the extent of variation among the values in a dataset.
The limitation of the range is that the range only considers the lower and upper limits, not the distribution of the other values in the dataset. Moreover, it doesn't talk about the number of data points. Range is affected by the outliers, as the extreme values can affect the range value.
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How to calculate Range in statistics?
As discussed, range is the difference between the upper and lower values. So, the formula to calculate the range is R = H - L, where R is the range, H is the maximum value, and L is the minimum value. Follow these steps to calculate the range -
Step 1: Arrange the data set in ascending order
Step 2: Identify the upper and lower limits from the dataset
Step 3: Finding the range using the formula; range = maximum value - Minimum value.
For instance, find the range of the given dataset: 5, 12, 8, 20, 15
Step 1: Arrange the data set in an order
That is 5, 8, 12, 15, 20
Step 2: Identify the upper and lower limits from the dataset
The upper limit is 20
The lower limit is 5
Step 3: Find the difference between the minimum and maximum value.
Range = 20 - 5 = 15
Real-world Applications of Range in Statistics
The concept of range has numerous applications across various fields. Now let’s learn a few applications of range in statistics.
- We use range to compare the prices of similar products; we use range to understand the price spread and to get an understanding of the budget.
- To analyze the performance of the students in an exam, we use range.
- To analyze the performance of the players in sports, range is used.
Common Mistakes and How to Avoid Them in Range of Statistics
Range is used to find the spread of the data. When finding the range in statistics students tend to make mistakes, let’s learn some common mistakes and ways to avoid them.
Mistake 1
Thinking that range as a measure of central tendency
Students sometimes think that range is a part of central tendency, but it is not, as range is the measure of dispersion. The range is about how the data is spread in the dataset.
Mistake 2
Failing to identify the upper and lower limits
When the numbers are not arranged in order, students feel difficult to identify the maximum and minimum values. So it is important to sort the data to identify the limits.
Mistake 3
Confusing range with interquartile range
Sometimes students tend to confuse the range with interquartile range, hence, it is significant for the students to understand the definition of it. The range is the difference between the upper and lower limit. Whereas the interquartile range is in the middle of the 50% of the dataset.
Mistake 4
Calculation errors
Simple mathematical errors are common among students and can lead to errors in range calculation. So always double-check each step of the calculation.
Mistake 5
Incorrect subtraction order
When calculating the range of a dataset, the range is the difference between the upper limit and lower limit. But sometimes, students subtract in the wrong order, by subtracting the lower limit with upper limit. So students should remember that range is the difference between the upper and lower limit.
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Solved Examples of Range in Statistics
Problem 1
A teacher recorded the ages of five students in a classroom: 12, 14, 15, 13, and 16 years old. Find the range of their ages.
The range of their ages is 4 years
Explanation
The given data in ascending order is 12, 13, 14, 15, 16
The upper limit is 16
The lower limit is 12
The range = 16 - 12 = 4
The range of their age is 4
Problem 2
The heights (in inches) of five basketball players are: 68, 72, 75, 70, and 78 inches. Find the range of their heights.
The range of their heights is 10 inches
Explanation
The given dataset in ascending order is 68, 70, 72, 75, 78
The upper limit is 78
The lower limit is 68
The range of heights = 78 - 68 = 10 inches
Problem 3
A shopkeeper recorded the number of customers visiting his shop over five days: 45, 38, 50, 42, and 47. Determine the range of customers.
The range of customers is 12
Explanation
The given dataset in ascending order is 38, 42, 45, 47, 50
The upper limit is 50
The lower limit is 38
The range of customers = 50 - 38 = 12
Problem 4
The temperatures (in °C) recorded in a city over five days are: 32, 29, 35, 31, and 30. Find the range of temperatures.
The range of the temperatures is 6 °C
Explanation
The given dataset in ascending order is 29, 30, 31, 32, 35,
The upper limit is 35
The lower limit is 29
The range of temperatures = 35 - 29 = 6 °C
Problem 5
A student recorded the number of pages read each day for a week: 20, 15, 18, 22, 25, 30, and 27. Find the range of pages read.
The range of pages read is 15 pages
Explanation
The given dataset in ascending order is 15, 18, 20, 22, 25, 27, 30
The upper limit is 30
The lower limit is 15
The range of pages read = 30 - 15 = 15
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FAQs on Range in Statistics
1.What is the range in statistics?
2.How is the range calculated?
3. What is the use of range?
4.Can the range be negative?
5.What does a high range indicate?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
