What the standard error tells you
The standard error of the mean is how much the sample mean would typically vary if you repeated the study. It is the building block of confidence intervals and t-tests. See how to calculate the standard error.
Worked examples
- From data: 12, 14, 15, 15, 16, 17, 18, 19, 21 has mean 16.33 and SD 2.74, so SE = 2.74 / √9 = 0.91.
- From SD and n: SD 20, n = 100: SE = 20 / 10 = 2.
- From a proportion: 52% of 1,000: SE = √(0.52 × 0.48 / 1000) = 0.0158, or 1.58 points.
SE or SD?
Report the SD to describe your data, and the SE or a confidence interval to show how precise an estimate is. Error bars can show either, so always label them. See standard deviation vs standard error.
In Excel: =STDEV.S(A1:A9)/SQRT(COUNT(A1:A9)). Excel has no built-in standard error function.
Frequently asked questions
How do you calculate standard error?
Divide the standard deviation by the square root of the sample size.
Does standard error decrease with sample size?
Yes, in proportion to the square root of n. Four times the data halves the standard error.
How do I calculate standard error in Excel?
Use =STDEV.S(range)/SQRT(COUNT(range)).