Standard error
Standard error is the standard deviation of an estimator's sampling distribution. It quantifies how much a sample statistic, such as a mean or regression coefficient, typically deviates from the true population value.
Also known asSE
See it move
A formula card presents SE(x̄) = s ÷ √n, where s is the sample standard deviation and n is the number of observations. Two numerical examples sit side by side: with s = 10 and n = 100 the standard error is 10 ÷ √100 = 1.0 unit, and with n = 400 it halves to 10 ÷ √400 = 0.5 units — confirming that precision grows with the square root of sample size. A footnote cautions that a small SE reflects estimation precision only and says nothing about whether the estimated quantity is practically important.
The formula
Variables
- Standard error of the sample mean
- Sample standard deviation
- Sample size
Estimates how far a sample mean typically falls from the true population mean. Used to construct confidence intervals and test statistics.