What is the standard error of the mean?

The standard error of the mean (SE of the mean) estimates the variability between sample means that you would obtain if you took multiple samples from the same population. The standard error of the mean estimates the variability between samples whereas the standard deviation measures the variability within a single sample.

For example, you have a mean delivery time of 3.80 days with a standard deviation of 1.43 days based on a random sample of 312 delivery times. These numbers yield a standard error of the mean of 0.08 days (1.43 divided by the square root of 312). Had you taken multiple random samples of the same size and from the same population the standard deviation of those different sample means would be around 0.08 days.

Use the standard error of the mean to determine how precisely the mean of the sample estimates the population mean. Lower values of the standard error of the mean indicate more precise estimates of the population mean. Usually, a larger standard deviation will result in a larger standard error of the mean and a less precise estimate. A larger sample size will result in a smaller standard error of the mean and a more precise estimate.

Minitab uses the standard error of the mean to calculate the confidence interval, which is a range of values likely to include the population mean.

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