Theoretically, computing the sampling distribution of any sample statistic is no different than computing the variance for a set of individual observations or scores. After computing the individual statistic for a very large number of samples or an infinite number of samples, we could calculate the mean of the particular sample statistic in question, subtract that mean from all of the individual instances, square those difference, sum those squared differences, and divide the total by the number of samples. The result is a sampling distribution for that statistic. The square root of that value is the standard error for that statistic. An important proviso is that all of the samples must be the same size.

The estimate of the variance in the sample means is called the sampling distribution of the mean and its square root is called the standard error of the mean. According to the Central Limits Theorem the mean of the sampling distribution of the means is equal to the mean of the population from which the scores were sampled.