Range in Statistics
2026-02-28 09:06 Diff
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Last updated on November 27, 2025

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 statistics, the range is used to describe the spread of data in a dataset. The range in math is the difference between the smallest and largest values. This simple calculation shows how much the values differ and gives a basic idea of the data’s overall spread.

However, the definition of range in math also comes with limitations. The range only considers the lower and upper values and does not account for how the other data points are distributed. It also ignores the number of data points in the dataset. Because of this, the range can be misleading when there are outliers, since excessively high or low values can significantly affect the result.

For example,

Consider the dataset as,

12, 18, 25, 30, 37

Highest value = 37

Lowest value = 12

Now,

The range = \(37–12 = 25\)

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 - \(\text{Range} = \text{Maximum value} - \text{Minimum value} \)

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; \(\text{Range} = \text{Maximum value} - \text{Minimum value} \).

For instance, find the range of the given dataset: \(5, 12, 8, 20, 15\)
 

Step 1: Arrange the data set in 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 = \(20 – 5 = 15\)

What is the Rule of Thumb?

According to the rule of thumb, most of the data values fall within four standard deviations, that is, two standard deviations above the mean and two standard deviations below the mean.
The formula for standard deviation (σ) is,

\(\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \)

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What are the Limitations of Range?

The range is easy to calculate, but it has several drawbacks:
 

  • It does not provide information about how many data points are in the dataset.
     
  • It cannot be used to determine other measures, like the mean, median, or mode.
     
  • It is highly sensitive to outliers, meaning extreme values can significantly change the range.
     
  • It is not suitable for open-ended distributions.

Range Formula

The formula used to calculate the range of a dataset is,

\(\text{Range} = \text{Maximum value} - \text{Minimum value} \)

In addition to this basic formula, there are specific methods for finding the range of both grouped and ungrouped data.

Range of Ungrouped Data

For continuous frequency distributions or grouped data, the range is calculated as the difference between the upper boundary of the highest class interval and the lower boundary of the lowest class interval. It is one of the simplest measures of dispersion and provides an overall idea of how spread out the observations are.

The formula to calculate the range for grouped data is:

Range = Upper class boundary of the highest interval - Lower class boundary of the lowest interval.

Range of Grouped Data

For continuous frequency distribution or grouped data, the range is the difference between the upper boundary of the highest class interval and the lower boundary of the lowest class interval. It is one of the simplest measures of dispersion and provides a clear picture of the data's overall spread.

The formula for calculating the range of grouped data is,

Range = Upper class boundary of the highest interval - Lower class boundary of the lowest interval.

Tips and Tricks to Master Range of Statistics

The range of statistics is a complex mathematical topic; however, with some tips and tricks, it can be better understood. Some valuable tips and tricks are mentioned below.
 

  • Make sure to carefully review your dataset to identify the actual highest and lowest values before calculating the range.
     
  • Put your numbers from smallest to largest or largest to smallest; it helps you easily find the smallest and largest values.
     
  • Big or small odd numbers can change the range, so make sure to check for any unusual values in your data.
     
  • When comparing two sets of data, a larger range indicates the values vary widely, while a smaller range suggests the data is steadier and consistent.
     
  • Try using the range with real-life examples such as temperature changes, exam marks, or stock prices. It helps you better understand the concept and see how it works in everyday situations.
  • Parents can use familiar situations, such as children’s heights in class, daily temperatures, or pocket money, to explain how a range shows the spread of values.
  • Teachers and parents can show children how to calculate the range for grouped data using class intervals.
  • Children can better understand the concept when it relates to their everyday life.

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.   

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.
  • Meteorologists use the range to show the difference between the highest and lowest temperatures in a day, week, or month to analyze climate patterns.
  • Teachers use the range of students’ marks to measure the variation in performance within a class or across multiple tests.

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.

Okay, lets begin

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.
 

Well explained 👍

Problem 2

The heights (in inches) of five basketball players are: 68, 72, 75, 70, and 78 inches. Find the range of their heights.

Okay, lets begin

 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.
 

Well explained 👍

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.

Okay, lets begin

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 = \(50 - 38 = 12\).
 

Well explained 👍

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.

Okay, lets begin

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 = \( 35 - 29 = 6 °C.\)
 

Well explained 👍

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.

Okay, lets begin

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 = \(30 - 15 = 15.\)

Well explained 👍

FAQs on Range in Statistics

1.What is the range in statistics?

The range is the measure of dispersion, it is the difference between the upper and lower limit of the dataset. 

2.How is the range calculated?

The range is calculated by subtracting the upper limit from the lower limit. 
 

3. What is the use of range?

Range is used to analyze how the data is spread in a dataset. 

4.Can the range be negative?

No, the range cannot be negative. Because the range is calculated by subtracting the upper limit from the lower limit. 

5.What does a high range indicate?

The high range indicates that there is a large spread between the smallest and largest values. 
 

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!