# standard error

## 1. sampling distribution

- Pick a statistic that can be calculated over a sample (like the sample mean)
- A simple consists of \(n\) observations \(x_1, x_2, ... x_n\)

- Then, over repeated samplings, we can build a distribution of the sample statistic
- This distribution has its own mean and variance

## 2. standard error

- Let \(\bar{x}\) be the random variable that corresponds with the sample mean over the samples that can be drawn
- Then, the standard deviation of this random variable is \(\sigma_{\bar{x}} = \sigma/\sqrt{n}\) where \(\sigma\) is the population standard deviation.