How to Calculate Range

Co-authored by David Jia

Last Updated: April 1, 2024 Fact Checked

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In statistics, range represents the difference between the highest value of a data set and the lowest value of a data set. The range shows how spread out the values in a series are. If the range is a high number, then the values in the series are spread far apart; if the range is a small number, then the values in the series are close to each other. If you want to know how to calculate range, just follow these steps.

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List the elements of your data set. To find the range of a set, you'll need to list all of the elements of the set so that you can identify the highest and lowest numbers. Write down all of the elements. The numbers in this set are: 20, 24, 25,19, 24, 28 and 14.^{[1]
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David Jia
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Expert Interview. 14 January 2021.}
- It can be easier to identify the highest and lowest number in the set if you list the numbers in ascending order. In this example, the set would be rearranged like this: 14, 19, 20, 24, 24, 25, 28.
- Listing the elements of the set in order can also help you make other calculations, such as finding the mode, mean, or median of the set.
^{[2]
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Research source} In this case, the lowest number in the set is 14 and the highest number is 28.^{[3]
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David Jia
Academic Tutor

Expert Interview. 14 January 2021.}

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Subtract the smallest number in your data set from the largest number. Now that you've identified the smallest and largest numbers in the set, all you have to do is subtract them from each other.^{[4]
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Research source} Subtract 14 from 28 (28 - 14) to get 14, the range of the set.^{[5]
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David Jia
Academic Tutor

Expert Interview. 14 January 2021.}
Once you've found the range, label it clearly. This will help you avoid confusing it with any other statistical calculations that you may need to make for the set, such as finding the median, mode, or mean.^{[6]
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What is the range of a list of numbers?

David Jia
Academic Tutor
David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

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Expert Answer

If you're given a set of data, find the smallest number, then the largest number. Subtract them from each other to get the range.

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What would be the range of these numbers - 8, -6, 0, 1, 3, 4, 20 be?

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First order the data from least to greatest, then subtract the smallest value from the largest value in the set.

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How do I calculate mean, median and mode?

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For mean, add all numbers up and divide them by how many numbers there are. For median, place all numbers in ascending order then find the middle number. For mode, find the most commonly-occurring number.

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The median value of any statistical data set represents the "middle" of the data set in terms of the data distribution, not its range. So although you might be tempted to assume that the median of a given data set is the range divided by 2--or halfway between the extremes of the range--that usually isn't the case. To find the correct median, you must list the data elements in order, then locate the element in the middle of the list. That element is the median. For example, if you have a list of 29 elements, the 15th element will be equidistant from both the top and bottom of the ordered list, so the 15th element is the median, no matter how its value relates to the range.

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You can also interpret "range" in algebraic terms, but first you have to grasp the concept of an algebraic function, or a set of operations on any given number. Since the function's operations can be performed on any number, even an unknown number, that number is represented by a letter variable, usually "x." The domain is the set of all possible input values you can substitute for that unknown number. The range of a function, then, is the set of all possible results you can get after inputting one of the domain values, and performing all the operations defined by the function. Unfortunately, there's no single way to calculate a function's range. Sometimes graphing the function or calculating several values will demonstrate a clear pattern. You can also use your knowledge of the function's domain to eliminate possible output values, or narrow down the data set that indicates the range.

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