How this calculator works
The standard error of a mean describes how a sample average would vary across repeated samples. With raw data, estimate sample variance using n - 1, take its square root and divide by sqrt(n). Summary mode starts with that sample SD directly. The result assumes independent observations from a common population and does not account for weighting, clustering, serial correlation or a large sampling fraction. A zero result from identical observed values does not establish that the broader population has no uncertainty.
Formula
Mean = sum(x_i)/n; s² = sum[(x_i - mean)²]/(n - 1); estimated SEM = s/sqrt(n).
Worked example
For observations 1 and 3, the mean is 2 and squared deviations total 2. Sample SD is sqrt(2), so SEM is 1. A sample SD of 6 with n = 9 gives SEM = 2.
Advertisement
Frequently asked questions
How is SEM different from SD?
SD describes individual observations. SEM describes the estimated variability of the sample average.
Can I use a single observation?
No. Estimating sample SD from raw data requires at least two observations.
Is one SEM a 95% confidence interval?
No. A confidence interval requires a suitable multiplier and assumptions; small samples commonly use a Student t multiplier.