Consider $n$ points $x_1,\ldots,x_n$ in $\mathbb{R}^n$.
How to find the best plane passes through the center of these points with following approach:
If we assume that the such plane has form $w.x-\gamma=0$ then distance between this plane and any points $x_i$ is equal $$D=\frac{\Vert w\cdot x_i-\gamma\Vert}{\Vert w\Vert}$$ and for the best plane passes through the center of these points the sum of all distances must be minimized.