  We present a detailed study of the coupling-constant-averaged
exchange-correlation hole density at a jellium surface, which we obtain in the
random-phase approximation (RPA) of many-body theory. We report contour plots
of the exchange-only and exchange-correlation hole densities, the integration
of the exchange-correlation hole density over the surface plane, the on-top
correlation hole, and the energy density. We find that the on-top correlation
hole is accurately described by local and semilocal density-functional
approximations. We also find that for electrons that are localized far outside
the surface the main part of the corresponding exchange-correlation hole is
localized at the image plane.
