Average

Pronunciation: /ˈæv rɪdʒ/ ?

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

mean=(a1+a2+a3+..an)/n

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 number.

References

  1. average. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=average&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.

More Information

  • McAdams, David. Arithmetic Mean. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Arithmetic Mean.
  • McAdams, David. Median. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Median (Statistics).
  • McAdams, David. Mode. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Mode.

Printed Resources

Cite this article as:


Average. 2010-01-04. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/average.html.

Translations

Image Credits

Revision History


2008-10-07: Expanded 'More Information' (McAdams, David.)
2008-06-26: Changed equations to LaTeX (McAdams, David.)
2008-03-25: Revised more information to match current standard.
2007-07-12: Initial Version (McAdams, David.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License