Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
The standard error of the mean (SEM) measures the accuracy with which a sample mean represents the population mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.
5 Must Know Facts For Your Next Test
The formula for SEM is $\text{SEM} = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the sample standard deviation and $n$ is the sample size.
SEM decreases as the sample size increases, indicating a more accurate estimate of the population mean.
SEM is used to construct confidence intervals for estimating population parameters.
A smaller SEM indicates less variability in the sampling distribution of the sample mean.
SEM is different from standard deviation; while standard deviation measures variability within a single sample, SEM measures how much those means vary between samples.