Standard deviation without square

For $(x_i)_{1 \leq i \leq N}$, the standard deviation is of course

$$\sigma = \sqrt{\frac{1}{N} \sum_i (x_i - m)^2},$$

where $m$ is the mean value of the $(x_i)$. We can say that the variance $\sigma^2$ is the average of the squared distance between each sample and the mean.

I know why the fact of having this square is helpful (for many formulas), and that $\sigma$ is much more used than :

$$\alpha =\frac{1}{N} \sum_i |x_i - m|,$$

that could seem a natural measure of the average distance between each sample and the mean.

Question:

Even if $\alpha$ is rarely used, is there a single-word name for $\alpha$ ?