The sampling distribution is what we use to help us decide whether a particular sample came from a given (or known) population. It tells us what to expect when we draw one sample from a larger population.

What is a sampling distribution?

A sampling distribution is the frequency distribution of the value of a statistic calculated on an infinite number of samples of a given size drawn from a known population.

How do we obtain a sampling distribution?

1. Choose a sample size.
2. Randomly draw a sample of that size from the population.
3. Calculate the statistic of interest on that sample.
4. Write down the value of the statistic.
5. Repeat this process an infinite number of times (or at least many times).
6. Gather together all of the values of your sample statistics.
7. Create a plot or graph using all of these values.

Now let's see this process in action.