Central limit theorem

The central limit theorem is what lets you use normal-based methods for means even when the underlying data are not normal. For example, individual household incomes are strongly right-skewed, yet the distribution of mean income from samples of 50 households is close to a bell shape. As the sample size $n$ grows, the sampling distribution of $\bar{x}$ (x-bar, the sample mean) approaches a normal shape centered at $\mu$ (mu) with standard deviation $\frac{\sigma}{\sqrt{n}}$ (sigma over root n). A common guideline is that $n \ge 30$ is large enough for many populations.