How to Calculate the Mean: Step-By-Step Guide

Quickly find the mean of the data with this user-friendly guide

Co-authored by Jake Adams

Last Updated: February 22, 2024 References

In mathematics, the "mean" is a kind of average found by dividing the sum of a set of numbers by the count of numbers in the set. ^{[1]
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Research source} While it isn't the only kind of average, the mean is the one most people think of when speaking about an average. You can use means for all kinds of useful purposes in your daily life, from calculating the time it takes you to get home from work, to working out how much money you spend in an average week. ^{[2]
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Determine the set of values you want to average. ^{[3]
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v161418_b01. Tuesday, January 24, 2023.} These numbers can be big or small, and there can be as many of them as you want. ^{[4]
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Research source} Just make sure you are using real numbers and not variables.
- Example: 2, 3, 4, 5, 6.
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Add your values together to find the sum. You can use a calculator, by hand, or a spreadsheet application to do so. ^{[5]
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- Example: $2+3+4+5+6=20$
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Count the number of values in your group. Count all of the numbers added up. Identical values should still be counted, meaning if you have values that repeat in your set, each one still counts in determining your total. Do not include the sum (answer) of all the numbers added up when counting the quantity of the values. ^{[6]
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- Example: 2, 3, 4, 5, and 6 make for a total of five values.
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Divide the sum of the set by the number of values. The result is the mean (a type of average) of your set. This implies that if each number in your set was the mean, they would add up to the same total. ^{[7]
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- Example: $20/5=4$ . Therefore, 4 is the mean of the numbers. You can check your calculations by multiplying the mean by the number of values in the set. In this case, multiply $4$ (the mean) by the $5$ (the number of values in the set) and your result will be $20$ ( $4*5=20$ ).

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What do I do if my mean/average has a remainder?

Donagan

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Convert the remainder to a decimal or fraction. For example: the average of 5, 12, and 17 is 34 ÷ 3, which is 11 with a remainder of 1. Convert the remainder to the fraction 1/3 or the decimal .33. Thus, the average is 11-1/3 or 11.33.

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How do I calculate the mode?

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It is the number in a set which appears most often. In the set {1 7 9 0 4 5 4}, 4 is the mode.

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How do I find the range?

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The range of a data set is the difference between the largest number and the smallest number in the set.

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Other kinds of averages include the median and mode . ^{[8]
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Research source} The mode is the value repeated most often in any set. The median is the number in a set with an equal quantity of values in the set greater and smaller than it. These averages will often produce different results than the mean from the same set of numbers. ^{[9]
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