Before a simple research question such as "What is the mean number of digits that can be remembered?" can be answered, it is necessary to specify the population of people to which it is addressed. The researcher could be interested in, for example, adults over the age of 18, all people regardless of age, or students attending high school. For the present example, assume the researcher is interested in students attending high school.

Once the population is specified, the next step is to take a random sample from it. In this example, let's say that a sample of 10 students were drawn and each student's memory tested. The way to estimate the mean of all high school students would be to compute the mean of the 10 students in the sample. Indeed, the sample mean is an unbiased estimate of μ, the population mean. But it will certainly not be a perfect estimate. By chance it is bound to be at least either a little bit too high or a little bit too low (or, perhaps, much too high or much too low).

For the estimate of μ to be of value, one must have some idea of how precise it is. That is, how close to μ is the estimate likely to be?