Mean Deviation

The mean deviation is the mean of the distances of the data from the data mean. The mean deviation of x1, x2,…, xn is

$\displaystyle {\frac{{\dsum\limits_{i=1}^{n}\left\vert x_{i}-\frac{\sum_{j=1}^{n}x_{j}}{%
\stackrel{\vspace{2pt}}{n}}\right\vert }}{{n}}}$

where the vertical bars denote absolute value. (Without the absolute values, this sum would be zero.) For example, the mean deviation of $\left\{\vphantom{
1,2,3,4,5}\right.$1, 2, 3, 4, 5$\left.\vphantom{
1,2,3,4,5}\right\}$ is

$\displaystyle {\frac{{\ \left\vert 1-3\right\vert +\left\vert 2-3\right\vert +\...
...-3\right\vert +\left\vert
4-3\right\vert +\left\vert 5-3\right\vert \ }}{{5}}}$ =  $\displaystyle {\frac{{6}}{{5}}}$

$\blacktriangleright$ Statistics + Mean Deviation

1, 2, 3, 4, 5, Mean deviation(s): ${\frac{{6}}{{5}}}$