The Standard Error (SE) of a sample statistic (such as the sample mean) is a measure of the variability associated with it. The SE is obtained as the standard deviation of the sampling distribution of the statistic. For the sample mean, the SE is calculated as the sample standard deviation divided by the square-root of the sample size.
Suppose the standard deviation of a random sample of 25 individual observations is 100. Then the standard error of Xbar:
The standard error of a statistic is important as it is used to calculate Confidence Intervals and perform significance tests.