What is a sampling distribution?

A sampling distribution describes the likelihood of obtaining each possible value of a statistic from a random sample of a population; in other words, what proportion of all random samples of that size will give that value. Suppose you measure the fill weights of a random sample of 10 boxes of cereal coming from the fill machine and calculate a mean of 370 g. Together with the population and the sample size, the sampling distribution describes the likelihood of getting this value or any other for the mean fill weight.

If you know the population, you can determine the sampling distribution. But you can still derive useful information about the sampling distribution without knowing the population. For example, even if you don't know the population, you might be able to say that there is an 85% certainty that the sample mean is within a certain number of standard deviations of the population mean. Or you might be able to say that, if the means of two populations are equal, the difference between sample means should fall between certain values.

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