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Mean Distribution

For an infinite population with mean mu, variance sigma^2, skewness gamma_1, and kurtosis excess gamma_2, the corresponding quantities for the distribution of means are

mu_(x^_)=mu
(1)
sigma_(x^_)^2=(sigma^2)/N
(2)
gamma_(1,x^_)=(gamma_1)/(sqrt(N))
(3)
gamma_(2,x^_)=(gamma_2)/N.
(4)

For a population of M (Kenney and Keeping 1962, p. 181),

mu_(x^_)^((M))=mu
(5)
sigma^2^((M))=(sigma^2)/N(M-N)/(M-1).
(6)

See also

Mean, Sample Variance Distribution

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References

Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, 1962.

Referenced on Wolfram|Alpha

Mean Distribution

Cite this as:

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

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