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arithmetic mean
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(Definition)
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If
 are real numbers, their arithmetic mean is defined as
The arithmetic mean is what is commonly called the average of the numbers. The value of  is always between the least and the greatest of the numbers  .
A generalization of this concept is that of weighted mean, also known as weighted average. Let
 be numbers whose sum is not zero, which will be known as weights. (Typically, these will be strictly positive numbers, so their sum will automatically differ from zero.) Then the weighted mean of
 is defined to be
In the special case where all the weights are equal to each other, the weighted mean equals the arithmetic mean.
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"arithmetic mean" is owned by drini. [ full author list (3) | owner history (1) ]
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See Also: geometric mean, harmonic mean, arithmetic-geometric-harmonic means inequality, general means inequality, weighted power mean, power mean, geometric distribution, root-mean-square, proof of general means inequality, proof of arithmetic-geometric-harmonic means inequality, derivation of geometric mean as the limit of the power mean, mean, a prime theorem of a convergent sequence, centre of mass of polygon
| Other names: |
average, mean |
| Also defines: |
weighted mean, weighted average |
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Cross-references: positive, strictly, weights, sum, numbers, real numbers
There are 105 references to this entry.
This is version 8 of arithmetic mean, born on 2001-10-20, modified 2006-11-11.
Object id is 405, canonical name is ArithmeticMean.
Accessed 29673 times total.
Classification:
| AMS MSC: | 11-00 (Number theory :: General reference works ) | | | 26D15 (Real functions :: Inequalities :: Inequalities for sums, series and integrals) |
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Pending Errata and Addenda
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