Find the minimum sum of distances between sets of points to a straight line in a plane
Given a line $L = b$, the distance from any point $(x, y)$ to $L$ is
$\left| y - b\right|$.
The sum of a distances for a set of points $S = \{(x_1, y_1), \dots,
(x_n, y_n)\}$ is then
$$\left| y_1 - b \right| + \cdots + \left| y_n - b \right|$$
which is minimized for which $b$?