Statistical significance of the median of a set of points on the plane

Abstract

The word median appears in two apparently different mathematical contexts.

In statistics it appears as a measurement of central position and in geometry as one of the lines determined by the barycenter. Why do we use the same word if they are apparently different things?

We can intuit a first relationship. In geometry, a medial line in a triangle passes through a vertex and splits the triangle into two equal areas. This property could be related to the definition of the median on the real line, but the intersection point of the medians is the barycenter, which turns out to be the arithmetic mean of the three vertices, understanding the barycenter as the centre of gravity or a figure’s centre of mass.