Sampling Distribution of the Mean



The sampling distribution of the mean is a very important distribution. In later chapters you will see that it is used to construct confidence intervals for the mean and for significance testing.

Given a population with a mean of μ and a standard deviation of σ, the sampling distribution of the mean has a mean of μ and a standard deviation of

,

where n is the sample size. The standard deviation of the sampling distribution of the mean is called the standard error of the mean. It is designated by the symbol: σM . Note that the spread of the sampling distribution of the mean decreases as the sample size increases.



An example of the effect of sample size is shown above. Notice that the mean of the distribution is not affected by sample size.

Click here for an interactive demonstration of sampling distributions.