\begin{definition}[Definition:Centroid of Set of Points/Definition 1]
Let $S = \set {A_1, A_2, \ldots, A_n}$ be a set of $n$ points in Euclidean space.
Let the position vectors of the elements of $S$ be given by $\mathbf a_1, \mathbf a_2, \dotsc, \mathbf a_n$ respectively.
Let $G$ be the point whose position vector is given by:
:$\vec {OG} = \dfrac 1 n \paren {\mathbf a_1 + \mathbf a_2 + \dotsb + \mathbf a_n}$
Then $G$ is known as the '''centroid''' of $S$.
\end{definition}