2.8 Normal

Under the central limit theorem, if we take samples from a random variable and calculate a summary statistic for each sample, that statistic is itself a random variable, and its mean converges to the true population statistic with more and more sampling.

The standard deviation of a sampled statistic is called the standard error of that statistic. In the case of the sampled mean, it is

\[SE = \frac{\sigma}{\sqrt{n}}\]