<P> In statistics, a sampling distribution or finite - sample distribution is the probability distribution of a given statistic based on a random sample . Sampling distributions are important in statistics because they provide a major simplification en route to statistical inference . More specifically, they allow analytical considerations to be based on the sampling distribution of a statistic, rather than on the joint probability distribution of all the individual sample values . </P> <P> The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of size n . It may be considered as the distribution of the statistic for all possible samples from the same population of a given size . The sampling distribution depends on the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used . There is often considerable interest in whether the sampling distribution can be approximated by an asymptotic distribution, which corresponds to the limiting case either as the number of random samples of finite size, taken from an infinite population and used to produce the distribution, tends to infinity, or when just one equally - infinite - size "sample" is taken of that same population . </P>

The sampling distribution of a proportion is called