standard error

问题如下：

What is the difference between the standard deviation of the sample data and the standard error of the sample mean?

解释：

When data are iid, the standard error of the mean is $\sigma/ \sqrt n$

where $\sigma$ is the standard deviation of the data. The standard error measures the estimation error in the sample mean. As the sample size grows the standard error converges to 0. The (population) standard deviation measures the dispersion in the data. It is a fixed value independent of the sample size.