# geometric mean

Geometric Mean^{}.

If ${a}_{1},{a}_{2},\mathrm{\dots},{a}_{n}$ are real numbers, we define their *geometric mean* as

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

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

Title | geometric mean |

Canonical name | GeometricMean |

Date of creation | 2013-03-22 11:50:46 |

Last modified on | 2013-03-22 11:50:46 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 7 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 11-00 |

Classification | msc 44A20 |

Classification | msc 33E20 |

Classification | msc 30D15 |

Related topic | ArithmeticMean |

Related topic | GeneralMeansInequality |

Related topic | WeightedPowerMean |

Related topic | PowerMean |

Related topic | ArithmeticGeometricMeansInequality |

Related topic | ProofOfArithmeticGeome |

Related topic | RootMeanSquare3 |

Related topic | ProofOfGeneralMeansInequality |

Related topic | DerivationOfZerothWeightedPowerMean |

Related topic | ProofOfArithmeticGeometricHarmonicMeansI |