Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Harmonic Mean |
Harmonic MeanNoun1. The mean of n numbers expressed as the reciprocal of the arithmetic mean of the reciprocals of the numbers. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
| Domain | Definitions |
Mathematics | The number of elements to be averaged divided by the sum of the reciprocals of the elements. Source: European Union. (references) |
Source: compiled by the editor from various references; see credits. | |
(From Wikipedia, the free Encyclopedia)
In mathematics, the harmonic mean is one of several methods of calculating an average.
The harmonic mean of the positive real numbers a1,...,an is defined to be
In certain situations, the harmonic mean provides the correct notion of "average". For instance, if for half the distance of a trip you travel at 40 miles per hour and for the other half of the distance you travel at 60 miles per hour (i.e. less time), then your average speed for the trip is given by the harmonic mean of 40 and 60, which is 48. Similarly, if in an electrical circuit you have two resistors connected in parallel, one with 40 ohms and the other with 60 ohms, then the average resistance is 48 ohms (i.e. if you replace each resistor by a 48 ohm resistor, the total resistance will stay the same). Typically the harmonic mean is appropriate for situations when the average of a rate is desired.
A "simple" formula for the harmonic mean of two numbers is to multiply the two numbers, and divide that quantity by the arithmetic mean of the two numbers. In mathematical terms:
This is essentially the same formula as above, only it is simpler for those people who, for example, want to write it as a calculator program.
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Harmonic mean."
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Expression | Frequency per Day |
harmonic mean | 13 |
| Source: compiled by the editor from various references; see credits. | |
| Language | Translations for "harmonic mean"; alternative meanings/domain in parentheses. | ||||||||||||||||||||||
Danish | harmonisk gennemsnit. (various references) | ||||||||||||||||||||||
Dutch | harmonisch gemiddelde. (various references) | ||||||||||||||||||||||
Finnish | harmoninen keskiarvo. (various references) | ||||||||||||||||||||||
French | moyenne harmonique. (various references) | ||||||||||||||||||||||
German | harmonisches Mittel, harmonischer Durchschnitt. (various references) | ||||||||||||||||||||||
Greek | αρμονικός μέσος όρος, αρμονικός μέσος, αρμονική μέση τιμή. (various references) | ||||||||||||||||||||||
Hungarian | harmonikus középérték. (various references) | ||||||||||||||||||||||
Italian | media armonica. (various references) | ||||||||||||||||||||||
Pig Latin | armonichay eanmay média harmónica. (various references) media armónica. (various references) harmoniskt medelvärde. (various references) | ||||||||||||||||||||||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "a-a-c-e-h-i-m-m-n-n-o-r" | |
-2 letters: enharmonic. | |
-3 letters: anchorman, anchormen, harmonica. | |
-4 letters: ammoniac, armonica, chainman, chainmen, chairman, chairmen, chimaera, choreman, harmonic, macaroni, marocain, mnemonic, monecian, noncrime, omniarch, ranchman, ranchmen. | |
-5 letters: acarine, acromia, aeonian, ammonia, ammonic, anaemic, archine, cannier, carinae, carmine, chimera, chinone, choanae, chorine, coremia, enchain, encomia, hammier, harmine, incomer, machine, macrame, mahonia, manioca, marchen, menorah, microhm, minorca, monarch, moneran, moraine, narcein, nomarch, ocarina, romaine, romance. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
Hexadecimal (or equivalents, 770AD-1900s) (references)48 61 72 6D 6F 6E 69 63 4D 65 61 6E |
| Leonardo da Vinci (1452-1519; backwards) (references)
|
Binary Code (1918-1938, probably earlier) (references)01001000 01100001 01110010 01101101 01101111 01101110 01101001 01100011 00100000 01001101 01100101 01100001 01101110 |
HTML Code (1990) (references)H a r m o n i c   M e a n |
ISO 10646 (1991-1993) (references)0048 0061 0072 006D 006F 006E 0069 0063 004D 0065 0061 006E |
Encryption (beginner's substitution cypher): (references)4267847981807569247716780 |
| 1. Definition 2. Expressions: Internet 3. Translations: Modern 4. Anagrams | 5. Orthography 6. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
