More About the Standard Error

The standard error $se$ corresponds to the standard deviation of the sample mean. Let us recall that if we take a sample $X_1$, $X_2$, ..., $X_n$, in which each each $X_i$ is a random variable with population standard deviation $\sigma$, then the sample mean

is also a random variable, with a standard deviation equal to $\frac{\sigma}{\sqrt n}$. This standard deviation of the sampling distribution of sample mean is called the standard error $s_e$.