The mean of the sampling distribution of the mean is the mean
of the population from which the scores were
sampled. Therefore, if a population has a mean,
Summary: This module discusses sampling distribution of the mean.
The sampling distribution of the mean was defined in our Introduction to Sampling Distributions. This discussion reviews some important properties of the sampling distribution of the mean that were introduced in the demonstrations in this chapter (Basic Demo, Sample Size Demo, and Central Limit Theorem Demo).
The mean of the sampling distribution of the mean is the mean
of the population from which the scores were
sampled. Therefore, if a population has a mean,
The variance of the sampling distribution of the mean is
computed as follows:
The standard error of the mean is the standard deviation of
the sampling distribution of the mean. It is therefore the
square root of the variance of the sampling distribution of
the mean and can be written as:
Given a population with a mean
The expressions for the mean and variance of the sampling
distribution of the mean are not new or remarkable. What is
remarkable is that regardless of the shape of the parent
population, the sampling distribution of the mean approaches a
normal distribution as
Figure 2 shows how closely the sampling distribution of the mean approximates a normal distribution even when the parent population is very non-normal. If you look closely you can see that the sampling distributions do have a slight positive skew. The larger the sample size, the closer the sampling distribution of the mean would be to a normal distribution.