Standard error of the mean.

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

1. The formula for SEM is $\text{SEM} = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the sample standard deviation and $n$ is the sample size.
2. SEM decreases as the sample size increases, indicating a more accurate estimate of the population mean.
3. SEM is used to construct confidence intervals for estimating population parameters.
4. A smaller SEM indicates less variability in the sampling distribution of the sample mean.
5. SEM is different from standard deviation; while standard deviation measures variability within a single sample, SEM measures how much those means vary between samples.

Review Questions

• What does SEM measure in relation to a population mean?
• How does increasing sample size affect SEM?
• Why is SEM important when constructing confidence intervals?

Related terms

Standard Deviation: A measure of the amount of variation or dispersion in a set of values.

Confidence Interval: A range of values derived from a dataset that is likely to contain the value of an unknown population parameter.

Sampling Distribution: The probability distribution of a given statistic based on a random sample.