How To Find The Range Of A Data Set (Formula And Examples)

By Indeed Editorial Team

Published 25 April 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

If you are trying to understand and examine the distribution and scattering of a data set, you usually use the measures of variability. One of these measures of variability is the range. Knowing why and how to find range can help you analyse the data and search for potential patterns in the data set. In this article, we discuss what range is, explore the steps to calculate it, understand the importance and limitation of finding the range and discover a few tips for calculating it, along with some examples.

What is the range of a data set?

In mathematics and statistics, the range is the difference between a data set's maximum and minimum value. The range of a data set shows how dispersed or scattered the data is. A small range implies lower variability in a data set, while a high range implies a higher variability. The formula for calculating the range is:

Range (R) = highest value – lowest value

Range (R) = maximum value – minimum value

Related: Top 15 Careers In Mathematics (And Salary Information)

How to find the range of a data set

To understand how to find the range, follow these three steps:

1. List the numbers of your data set

To find the range of a data set, list all the numbers to identify the highest and lowest number. For instance, if the numbers in a data set are 12, 45, 67, 81, 54, 20, 25, it can be challenging to find the highest and lowest number. So, arrange these numbers in ascending order to make the calculation simpler. The numbers in the ascending order are:

12, 20, 25, 45, 54, 67, 81.

Additionally, listing your data in ascending order can make calculating the mean, median and mode of a data set easier.

Related: How To Find Average: A Step-by-Step Guide With Examples

2. Find the highest and lowest number in your data set

After listing numbers in ascending order, find the highest and lowest number in your data set. For example, if the data in ascending order is:

12, 20, 25, 45, 54, 67, 81

The highest value or number is 81 and the lowest number is 12.

3. Calculate the difference between these numbers

After knowing the highest and lowest number in your data set, use the formula to calculate the range. The formula for calculating the range is:

Range = highest value – the lowest value

Using the values from the above examples, the highest number is 81 and the lowest number is 12:

Range = 81 – 12 = 69

What is the importance of finding range?

The importance of finding the range includes:

Searching for patterns

Often, you calculate the range across multiple data sets to search for potential data patterns. For instance, if a women's clothing company calculates the range of their product reviews, they might discover that the range increases for their pure cotton wear versus rayon wear. This might mean that customers are leaving critical reviews for clothes that shrink on the first wash compared to clothes that last for a long time.

Analysing information

After knowing the range of your data set, you can further analyse the information it provides. For instance, if a company considers the range of salary hikes of employees, they can calculate the monetary distance between the highest-paid hike and lowest-paid hike in the organisation. Using the range, companies understand how the responsibilities and job performance of employees who received the highest and lowest hike differ. Companies can then renegotiate the salary hike with employees.

Identifying business growth

Calculating growth can help in determining the potential growth of a business. Knowing the potential growth can help in creating strategies to accelerate it. For instance, when a business wants to determine their sales growth, they can find the range in their set of sales data to get a rough estimate.

Related: How To Calculate Growth Rate Using Different Methods

Understanding progress

While calculating range, you can even determine the company's progress. For instance, a company evaluates the performance review of employees every quarter to understand whether employee performance increased or decreased. To do this, the company determines the range of scores. If the range decreased compared to the previous quarter, it shows an improvement in employee performance. If the range increases, it shows a decline in employee performance and a company might create a strategy to provide training to employees.

Calculating other mathematical equations

You can use the range of a data set to calculate other critical mathematical equations, such as standard deviation (SD). SD helps you understand the spread in a data set. Rather than using an overly complicated formula for calculating SD, you can use the ‘range rule' formula. The range of a data set is fundamental to this calculation.

What are some applications of range?

Statisticians and data scientists widely use the range of a data set to make some critical business decisions. Even though there are limitations for using the range for measuring the distribution of data, it does set boundaries for the values. So, the range is useful when measuring a variable with either a critically low or high threshold value you cannot cross. By calculating the range, you determine whether the highest or lowest value broke the threshold. It can also help detect any errors that might occur when entering data.

What are some limitations of range?

Even though the range is an essential metric for calculating the spread of data, it has some limitations, including:

  • It does not give information about the number of data points.

  • It can give a misleading value if the data has some outliers.

  • You cannot use range for understanding open-ended distribution.

  • You cannot use range for calculating the mean, mode or median.

  • The value of the range does not change even if you change all the terms between the highest and lowest values.

Tips for calculating range

Here are a few tips for calculating the range of a data set:

Organise your data

Often, you might receive data in random order and calculating the range of such data set can be challenging. So, every time you receive data, sort and list your data from the smallest to the largest value. You can easily find numbers you want to calculate the range.

Understand the outliers in your calculation

Often, the difference between the largest and the smallest number might vary. Though this might be a random occurrence, keep track of such outliers. When analysing your data for making a strategic business decision, these outliers can come useful. For example, in this data set:

420, 500, 650, 1000, 2020, 4020

The range of the data set is:

Range = 4020 – 420 = 3600

When analysing the data, it shows that the range is not an accurate reflection of the collected data.

Consider the negative values

When using negatives in the range calculation, focus on considering the negative value. Use the largest negative value as the smallest value and the smallest negative value as the highest value of the data set. For example, in the following data set:

–50, –40, –25, –20

–20 is the highest value and –50 is the lowest value.

Range = –20 – (–50) = 30

Also, the range of a data set can never be negative because you subtract a lower value from a higher value.

Examples of calculating range

Here are a few examples to help you understand how to find the range of a data set:

Example 1

A company wants to determine the range of its stock price over the last five days.

The company's data set is: ₹320, ₹420, ₹510, ₹620, ₹700

Highest value = ₹700

Lowest value = ₹320

Range = ₹700 – ₹320 = ₹380

Example 2

An entrance exam for engineering college has a negative marking system for every wrong answer a student gives. A coaching institution wants to determine the range of the entrance exam's score of the last ten students.

The entrance exam's score data set is: –40, –35, –32, –29, –28, –26, –25, –21, –19, –15

Highest value = –15

Lowest value = –40

Range = –15 – (–40) = 25

Example 3

A company wants to understand the range of sales in the past 10 days.

Their data set is: ₹40,000; ₹55,000; ₹62,000; ₹63,000; ₹63,500; ₹65,000; ₹68,000; ₹70,000; ₹72,250; ₹86,000.

Highest value = ₹86,000

Lowest value = ₹40,000

Range = ₹86,000 – ₹40,000 = ₹46,000

Example 4

A company wants to understand the range of its monthly spending on vending machines in the past five years.

Their data set is: ₹21,500; ₹18,890; ₹19,275; ₹26,700; ₹24,450

Organise the data in ascending order: ₹18,890; ₹19,275; ₹21,500; ₹24,450; ₹26,700

Highest value = ₹26,700

Lowest value = ₹18,890

Range = ₹26,700 – ₹18,890 = ₹7,810

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