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Population Mean


The mean of a distribution with probability density function P(x) is the first raw moment mu_1^', defined by

 mu=<x>,
(1)

where <f> is the expectation value.

For a continuous distribution function, the population mean is given by

 mu=intP(x)f(x)dx,
(2)

where <x> is the expectation value. Similarly, for a discrete distribution,

 mu=sum_(n=0)^NP(x_n)f(x_n).
(3)

The population mean of a distribution is implemented in the Wolfram Language as Mean[dist].

The sample mean is an unbiased estimator for the population mean.


See also

Arithmetic Mean, Mean, Population Variance, Sample Mean

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Cite this as:

Weisstein, Eric W. "Population Mean." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PopulationMean.html

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