Statistics
Standard error of the mean
The standard deviation of the sample mean. Shrinks with the square root of the sample size.
The Formula
SE = s / sqrt(n)
The standard deviation of the sample mean. Shrinks with the square root of the sample size.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| SE | Standard error | same as data | Spread of the sample mean across repeated samples. |
| s | Standard deviation | same as data | Standard deviation of the sample. |
| n | Sample size | count | Number of observations. |
What Each Symbol Means
SEsame as data
Standard error
Spread of the sample mean across repeated samples.
ssame as data
Standard deviation
Standard deviation of the sample.
ncount
Sample size
Number of observations.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a confidence interval page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Confidence Interval, filed under Math. Every number the guide produces comes from substituting into this one line.