请输入您要查询的字词:

 

单词 Mean
释义

mean


Loosely speaking, a mean is a way to describe a collectionMathworldPlanetmath of numbers suchthat the mean in some sense describe the “averageMathworldPlanetmath” entry of these numbers.The most familiar mean is the arithmetic mean, and unless otherwise noted, by mean,we always mean the arithmetic mean.

Example

The mean of the numbers {1, 2,,n} is n+12.

Mathematically, we define a mean as follows:

Definition

A mean is a functionMathworldPlanetmath f whose domain is the collection ofall finite multisets of and whose codomain is ,such that

  • f is a homogeneous function of degree 1.  That is, if {x1,,xn} is a multiset, then

    f({λx1,,λxn})=λf({x1,,xn}),λ0.
  • For any set S={x1,,xn} of real numbers,

    min{x1,,xn}f(S)max{x1,,xn}.

Pythagoras identified three types of means: the arithmetic mean (http://planetmath.org/ArithmeticMean), the geometricmeanMathworldPlanetmath, and the harmonic meanMathworldPlanetmath. However, in the sense of the above definition,there is a wealth of ther means too. For instance, the minimum function and maximumfunctions can be seen as “trivial” means. Other well-known means include:

  • median,

  • mode,

  • generalized meanMathworldPlanetmath

  • power meanMathworldPlanetmath

  • Lehmer meanMathworldPlanetmath

  • arithmetic-geometric meanDlmfDlmfMathworldPlanetmath,

  • arithmetic-harmonic mean,

  • harmonic-geometric mean,

  • root-mean-squareMathworldPlanetmath (sometimes called the quadratic mean),

  • identric mean,

  • contraharmonic mean,

  • Heronian meanMathworldPlanetmath,

  • Cesaro mean,

  • maximum function, minimum function (http://planetmath.org/MinimalAndMaximalNumber)

Titlemean
Canonical nameMean
Date of creation2013-03-22 12:43:43
Last modified on2013-03-22 12:43:43
Ownermatte (1858)
Last modified bymatte (1858)
Numerical id16
Authormatte (1858)
Entry typeDefinition
Classificationmsc 11-00
Classificationmsc 62-07
Related topicArithmeticMean
Related topicGeometricMean
Related topicContraharmonicProportion
Related topicOrderOfSixMeans
Related topicAverageValueOfFunction
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 6:48:51