An Etymological Dictionary of Astronomy and Astrophysics

A statement about the characteristics of the sampling distribution of means of → random samples from a given → statistical population. For any set of independent, identically distributed random variables, X₁, X₂,…, X_n,
with a → mean μ and → variance σ², the distribution of the means is equal to the mean of the population from which the samples were drawn. Moreover, if the original population has a → normal distribution,
the sampling distribution of means will also be normal. If the original population is not normally distributed, the sampling distribution of means will increasingly approximate a normal distribution as sample size increases.

See also: → central; → limit; → theorem.