How this calculation works
The standard error of a sample mean estimates how much that mean would vary across repeated samples under the usual independent-observation model. Enter an already calculated sample standard deviation and the number of observations used to obtain it. This is uncertainty in a mean, not spread among individual measurements.
Worked example
This example uses illustrative inputs. Your current result is shown above.
With a sample standard deviation of 15 and n = 100, √100 = 10. Standard error = 15 ÷ 10 = 1.5 in the same unit as the measurements.
Assumptions and limits
- Use the sample standard deviation, not the variance, in the deviation field.
- The simple formula assumes independent observations; clustered, correlated or weighted samples can need a different estimator.
- A sample size of one is arithmetically accepted if a deviation is supplied, but a sample deviation cannot be estimated from one observation alone.
Questions people ask
Why does increasing sample size lower the standard error?
The divisor is √n. With the same spread, four times as many independent observations halves this estimate of uncertainty in the mean.
Is this a 95% confidence interval?
No. An interval also needs a confidence level, distributional assumptions and an appropriate critical value, often from a t distribution when the population spread is unknown.