Use this selection to calculate a confidence interval around a mean if you know the sample size and standard deviation.

The standard error of the mean is estimated from the standard deviation and the sample size. It is used to establish the confidence interval (the range within which we would expect the mean to fall in repeated samples taken from the population). The standard error of the mean is an estimate of the standard deviation of those repeated samples.

The formula for the standard error of the mean provides an accurate estimate when the sample size is very small compared to the size of the population. In market research, this is usually the case since the populations are quite large. Thus, in most situations the population size may be left blank because the population is very large compared to the sample. However, when the sample is more than ten percent of the population, the population size should be specified so that the finite population correction factor can be used to adjust the estimate of the standard error of the mean.

Example

Suppose that an organization has 5,000 members. Prior to their membership renewal drive, 75 members were randomly selected and surveyed to find out their priorities for the coming year. The mean average age of the sample was 53.1 and the unbiased standard deviation was 4.2 years. What is the 90% confidence interval around the mean? Note that the population size can be left blank because the sample size of 75 is less than ten percent of the population size.