Sampling distribution of the sample mean

Picture taking every possible sample of size $n$ and recording $\bar{x}$ (x-bar, the sample mean); the pile of those values is the sampling distribution. Its center is the population mean, $\mu_{\bar{x}} = \mu$ (mu), and its spread is $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$ (sigma over the square root of n). If a population has $\mu = 500$ and $\sigma = 100$, samples of $n = 25$ give sample means centered at $500$ with standard deviation $100/\sqrt{25} = 100/5 = 20$. The shape is normal whenever the population is normal, and approximately normal for $n \ge 30$ by the central limit theorem.