Centroid

Noun

1. The point at which gravitational force (or other universally and uniformly acting force) may be supposed to act on a given rigid, uniformly dense body; the centre of gravity or centre of mass.
2. The point of intersection of the three medians of a given triangle; the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of the three vertices.
3. the point whose (Cartesian) coordinates are the arithmetic mean of the coordinates of a given finite set of points.
4. An analogue of the centre of gravity of a nonuniform body in which local density is replaced by a specified function (which can take negative values) and the place of the body's shape is taken by the function's domain.

   "The centroid of an arbitrary function f {\displaystyle f} is given by ∫ x f ( x ) d x ∫ f ( x ) d x {\displaystyle {\frac {\int xf(x)dx}{\int f(x)dx}}} , where the integrals are calculated over the domain of f {\displaystyle f} ."

5. the arithmetic mean (alternatively, median) position of a cluster of points in a coordinate system based on some application-dependent measure of distance.