Editing Sampling distribution (section)

==Introduction==
The '''sampling distribution''' of a statistic is the [[probability distribution|distribution]] of that statistic, considered as a [[random variable]], when derived from a [[random sample]] of size <math>n</math>. It may be considered as the distribution of the statistic for ''all possible samples from the same population'' of a given sample size. The sampling distribution depends on the underlying [[probability distribution|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.

For example, consider a [[normal distribution|normal]] population with mean <math>\mu</math> and variance <math>\sigma^2</math>. Assume we repeatedly take samples of a given size from this population and calculate the [[arithmetic mean]] <math> \bar x</math> for each sample – this statistic is called the [[sample mean]]. The distribution of these means, or averages, is called the "sampling distribution of the sample mean". This distribution is normal <math> \mathcal{N}(\mu, \sigma^2/n)</math> (''n'' is the sample size) since the underlying population is normal, although sampling distributions may also often be close to normal even when the population distribution is not (see [[central limit theorem]]). An alternative to the sample mean is the sample [[median]]. When calculated from the same population, it has a different sampling distribution to that of the mean and is generally not normal (but it may be close for large sample sizes).

The mean of a sample from a population having a normal distribution is an example of a simple statistic taken from one of the simplest [[statistical population]]s. For other statistics and other populations the formulas are more complicated, and often they do not exist in [[Closed-form expression|closed-form]]. In such cases the sampling distributions may be approximated through [[Monte-Carlo simulation]]s,<ref>{{cite book|last=Mooney|first=Christopher Z.|title=Monte Carlo simulation|year=1999| publisher=Sage|location=Thousand Oaks, Calif.|isbn=9780803959439|url = https://books.google.com/books?id=xQRgh4z_5acC|page=2}}</ref> [[Bootstrapping (statistics)|bootstrap]] methods, or [[asymptotic distribution]] theory.