Let $X$ be a random variable with mean $\mu$ and probability density function $f(x)$.

The standard deviation $\sigma$ is usually defined as the root of the variance:

$$\sigma = \sqrt{\int\_{-\infty}^\infty (x - \mu)^2 f(x) \,dx}$$

But how would one interpret the following term:

$$\int\_{-\infty}^\infty |x - \mu| f(x) \,dx \,\,?$$

Surely this expression is not equal to $\sigma$?