Standard Error Calculator
Calculate the standard error of the mean from standard deviation and sample size.
Standard error formula
SEM = s / √n. Standard error describes how precisely a sample mean estimates the population mean.
What Standard Error Measures
Standard error describes the estimated variability of a sample mean from sample to sample. It becomes smaller as sample size increases, assuming the underlying variability remains similar.
Standard Error Example
If a sample standard deviation is 20 and the sample size is 100, the standard error of the mean is 20 divided by the square root of 100, giving 2.
Why Standard Error Matters
Standard error is used in confidence intervals and many hypothesis tests. It is different from standard deviation: standard deviation describes spread among observations, while standard error describes uncertainty in an estimated mean.
Frequently Asked Questions
Does a larger sample reduce standard error?
Yes. Increasing sample size generally reduces the standard error.
Is standard error the same as standard deviation?
No. They describe different kinds of variability.
Can standard error be zero?
It can be zero only when the relevant sample variability is zero.
Standard Error vs. Data Spread
The standard error of the mean estimates how much a sample mean would vary across repeated samples under the model. It commonly equals sample standard deviation divided by the square root of sample size. It is different from standard deviation, which describes variation among individual observations.
Methodology, Assumptions and Interpretation
Standard error of the mean is commonly s/√n when the sample standard deviation estimates population variability. It measures uncertainty in the estimated mean, not the spread of individual observations, and decreases as sample size grows under comparable sampling conditions.