Each point owns the land nearer to it than to any other. Weigh three rain gauges by that land, and the average rises from 20.7 to 28.6 mm.

A Voronoi diagram splits a map so every spot belongs to its nearest point. Mathematicians say Voronoi cells, Esri's tool says Thiessen polygons, and Esri also calls them proximal zones. The borders are perpendicular bisectors, drawn from a Delaunay triangulation, and they only mean something in a projected coordinate system.