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# geometric mean

Geometric Mean.

If $a_{1},a_{2},\ldots,a_{n}$ are real numbers, we define their *geometric mean* as

$G.M.=\sqrt[n]{a_{1}a_{2}\cdots a_{n}}$ |

(We usually require the numbers to be non negative so the mean always exists.)

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Related:

ArithmeticMean, GeneralMeansInequality, WeightedPowerMean, PowerMean, ArithmeticGeometricMeansInequality, ProofOfArithmeticGeome, RootMeanSquare3, ProofOfGeneralMeansInequality, DerivationOfZerothWeightedPowerMean, ProofOfArithmeticGeometricHarmonicMeansI

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## Mathematics Subject Classification

11-00*no label found*44A20

*no label found*33E20

*no label found*30D15

*no label found*

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## Comments

## Additional References

You may also be interested to read about averages, weighted averages, and means in the following book and article.

* Jane Grossman, Michael Grossman, Robert Katz. "Averages: A New Approach", ISBN 0977117049, 1983. (Available for reading at Google Book Search:

http://books.google.com/books?q=%22Non-Newtonian+Calculus%22&btnG=Search...).

* Michael Grossman and Robert Katz. "A new approach to means of two positive numbers", International Journal of Mathematical Education in Science and Technology, Volume 17, Number 2, March 1986, pages 205 - 208.