Standard Error Calculator
The standard error of the mean: standard deviation ÷ √n.
Result
Standard error
2.7386
How it works
The standard error of the mean measures how precisely your sample average estimates the true population average: SE = standard deviation ÷ √n. With an SD of 15 and 100 observations, the SE is 1.5. Do not confuse it with the standard deviation. The SD describes how spread out the individuals are — it does not shrink as you collect more data. The SE describes how reliable your *average* is, and it does shrink: more data means a steadier estimate of the mean. The √n in the denominator sets the price of precision: to halve the standard error you need four times the sample. The SE is also the engine behind confidence intervals, which typically span the mean ± about 1.96 SE for 95% confidence.
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Frequently asked questions
SD vs standard error?
SD measures spread of the data; standard error measures spread of the sample mean.
How do I reduce it?
Increase the sample size — the standard error falls with the square root of n.
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