Pronunciation: /ˈæv.rɪdʒ/ Explain

The term average is not mathematically exact, as it can mean one of several types of operations that generate the center of a set. In arithmetic, average usually refers to the arithmetic mean. In statistics and probability, average can refer to the median or mode. A synonym for average is mean. Mean means the same thing as average.

To find the arithmetic mean of a set of numbers, add all the numbers together and divide by how many numbers there are in the set. The formula for arithmetic mean is


For example, the arithmetic mean of { 3, 7, 8, 12 } is (3+7+8+12)/44 = 30/4 = 7.5.

The median is the middle number of a set of numbers. To find the median, sort the set of numbers. Find the middle value (if the number of numbers is odd), or the arithmetic mean of the middle two values (if the number of numbers is even). These values are the median.

The mode is the most common value. In the set { 1, 3, 3, 5, 8, 14 } the mode is 3 because it appears the most often. If two or more values appear with the same frequency and most often, the mode will be all these values.

The geometric mean of a set of n numbers is the nth root of the product of the numbers.


  1. McAdams, David E.. All Math Words Dictionary, average. 2nd Classroom edition 20150108-4799968. pg 22. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

  • McAdams, David E.. Arithmetic Mean. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. https://www.allmathwords.org/en/a/arithmeticmean.html.

Cite this article as:

McAdams, David E. Average. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/average.html.

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Revision History

4/12/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/15/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
10/7/2008: Expanded 'More Information'. (McAdams, David E.)
6/26/2008: Changed equations to LaTeX. (McAdams, David E.)
3/25/2008: Revised more information to match current standard. (McAdams, David E.)
7/12/2007: Initial Version. (McAdams, David E.)

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