Harmonic Mean

Pronunciation: /hɑrˈmɒn.ɪk min/ Explain

A harmonic mean is a type of average. It is especially useful for rates and ratios. A rate is a value in one dimension divided by a value in another dimension such as kilometers per hour. The formula for the harmonic mean is:

H= n/(1/x1 + 1/x2 + 1/x3 + ... + 1/xn)
where xi is the ith value in the dataset and n is the number of values in the dataset.


  1. McAdams, David E.. All Math Words Dictionary, harmonic mean. 2nd Classroom edition 20150108-4799968. pg 89. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Harmonic Mean. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/h/harmonicmean.html.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/16/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
10/25/2010: Initial version. (McAdams, David E.)

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