Module 4 · Sampling & CLT · Topic 6

Standard Error

Standard Error (SE). The standard error is the standard deviation of the sampling distribution. It measures how much a sample statistic typically varies from sample to sample.

Interpreting SE. A smaller SE means sample means are tightly clustered around μ, so each sample gives a precise estimate. SE decreases as n increases, meaning larger samples yield more precise estimates.

Open the interactive lesson All topics

Key formulas

SE of the Mean

SE = σ / √n (when σ is known) or SE = s / √n (when using the sample standard deviation)

From the Sampling & CLT formula sheet

Standard Error of xbar: SE_xbar = sigma / sqrt(n) — Standard deviation of the sampling distribution of the sample mean.

See the full formula reference

Worked example

Effect of Sample Size

With σ = 10: n = 25 gives SE = 2, n = 100 gives SE = 1, n = 400 gives SE = 0.5. Quadrupling the sample size halves the standard error.

Related glossary terms

Parameter: A number that describes an entire population. Example: The true mean height of all students at a university.
Statistic: A number computed from a sample. Example: The mean height of 80 sampled students.
Standard Error: The standard deviation of a statistic across repeated samples. Example: The standard error of xbar is sigma divided by sqrt(n).

Browse the full glossary

Go interactive

Work this topic in StatRise

Start with the free descriptive-statistics module and daily practice; this module's tracked lesson unlocks with Premium.

Sampling & CLT lesson (Premium)Distributions calculators Sampling & CLT simulation (free)Practice questions

Keep reading