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harmonic mean

American  

noun

Statistics.

  1. the mean obtained by taking the reciprocal of the arithmetic mean of the reciprocals of a set of nonzero numbers.

harmonic mean British  

noun

  1. the reciprocal of the arithmetic mean of the reciprocals of a set of specified numbers: the harmonic mean of 2, 3, and 4 is 3( 1/ 2 + 1/ 3 + 1/ 4 ) –1 = 3 6/ 13

"Collins English Dictionary — Complete & Unabridged" 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
harmonic mean Scientific  

  1. The reciprocal of the arithmetic mean of the reciprocals of a specified set of numbers.

Etymology

Origin of harmonic mean

First recorded in 1880–85

Example Sentences

Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com.

Once we had those three numbers for each of the starting Super Bowl quarterbacks, we averaged them together using the harmonic mean rather than a simple average.

From Washington Post • Feb. 3, 2021

Eventually, they categorized proportions into 10 different classes, with names like the harmonic mean.

From "Zero: The Biography of a Dangerous Idea" by Charles Seife

The line P1P2 is also called the harmonic mean between AP2 and P2B, and the points A, P1, B, P2 are said to form an harmonic range.

From The Teaching of Geometry by Smith, David Eugene

Definitions and idiom definitions from Dictionary.com Unabridged, based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

Idioms from The American Heritage® Idioms Dictionary copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.