# The Standard Error As the sampling process is random, the sample average $\bar{x}_n$ will also be random. How far off from $\mu$ will the sample average be? This is given by the **standard error**. The **standard error (SE)** of a statistic tells you how far off a statistic will be from its expected value. It is given as follows: $SE(\bar{x}_n) = \frac{\sigma}{\sqrt{n}}$ - The standard error becomes smaller as the sample size $n$ grows in size - The formula for the standard error does not depend on the size of the population, only on the size of the sample #todo/primary - [x] What does this have to do with [[AB Testing#AB Testing Procedure#3. **Design the Experiment**]] - [x] Why does the standard error for the sum go up while the average goes down?