Finite point set/Center of gravity/Definition

For a set of ${\displaystyle {}n}$ points ${\displaystyle {}P_{1},\ldots ,P_{n}}$ in an affine space ${\displaystyle {}E}$ over a real vector space ${\displaystyle {}V}$, the barycentric combination

${\displaystyle {\frac {1}{n}}P_{1}+{\frac {1}{n}}P_{2}+\cdots +{\frac {1}{n}}P_{n}}$

is called the center of gravity of these points.