Samples from the same population likely have different variables affecting them.

This is a collection of sample means for all of the possible random samples of a particular size (n) that can be obtained from a population,

This is constructed by selecting samples, finding the sample mean, and adding the means to a frequency distribution.

The general characteristics of the frequency distribution should look like:

1. The sample means should be clustered around the population mean as most should be representative of the population.

2. The sampling distribution should resemble that of a normal distribution.

3. The larger the sample size, the closer the mean of this (denoted by μ_{M}) should be to the population mean. (larger n should cluster close to the population mean, small sample sizes should have a more scattered distribution.

This distribution, according to the Central Limit Theorem, is almost perfectly normal if 1) the population from which the samples are selected is a normal distribution, and 2) the the sample size n is relatively large (>=30).