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How to use
Standard error describes the sampling variability of an estimator. This calculator handles the standard error of a mean from s and n, and of a proportion from p and n.
- Choose mean or proportion mode.
- For a mean, enter sample standard deviation s and sample size n.
- For a proportion, enter p as a percentage and sample size n.
- Review SE and the clearly labeled approximate 95% normal margin 1.96×SE.
How it is calculated
Example
Example: with s=12 and n=36, SEM=12/√36=2. With p=40% and n=100, proportion SE≈4.90 percentage points.
Important notes
The displayed 95% margin is a simple normal approximation, not a substitute for a confidence-interval method suited to the problem. Proportion normal approximations can be poor with small expected counts.
Worked examples and interpreting results
Sample standard deviation 10 with size 25 gives mean standard error 2. Increasing size to 100 while keeping standard deviation 10 reduces it to 1.
| Case | Calculation | Result |
|---|---|---|
| For sample size 25 | 10 ÷ √25 | 2 |
| For sample size 100 | 10 ÷ √100 | 1 |
How to check the result
Select mean standard error. Standard deviation describes observation spread; standard error describes precision of the estimated mean. Dividing by square root of size assumes independent observations.
Frequently asked questions
Standard deviation versus standard error?
Standard deviation describes spread in observations; standard error describes sampling variation of an estimator such as the mean.
Why does SE shrink as n grows?
For a mean, SE is proportional to 1/√n, so larger samples reduce sampling uncertainty.
Does 1.96×SE always give a valid confidence interval?
No. It is a normal approximation and some settings require a different method.