Geometric Mean

Pronunciation: /ˌdʒi əˈmɛt rɪk min/ Explain

The geometric mean of a set of numbers {a1, a2, a3, ..., an} is the nth root of the product of the numbers in the set.[1]

M= nth root (a1*a2*a3*...*an)
The geometric mean of {1, 4, 6} is:
M=3rd root(1*4*6) = 3rd root(24) is about 2.884499.
A geometric mean is also called a mean proportional.


  1. geometric mean. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/6/2018. mean.
  2. mean proportional. Merriam-Webster Online Dictionary. Merriam-Webster. Last Accessed 9/2/2018.
  3. Lodge, Sir Oliver, F.R.S.. Easy Mathematics, Mainly Arithmetic. pg 340. Easy Mathematics. MacMillan and Company, Ltd.. 1906. Last Accessed 8/6/2018.
  4. Young, J. W. A. and Jackson, Lambert L.. A Second Course in Elementary Algebra. pp 178. D. Appleton and Company. 1910. Last Accessed 8/6/2018. Buy the book

Cite this article as:

McAdams, David E. Geometric Mean. 9/2/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

7/10/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/6/2010: Added "References". (McAdams, David E.)
4/18/2009: Initial version. (McAdams, David E.)

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