We give the first determination of the observed peculiar velocity distribution function for a representative sample of galaxies (within 50 Mpc (H=100) of the Local Group), which includes a wide range of clustering properties. We explore in detail the effects of uncertainties in sampling and in distance measures on the estimated distribution function. The observed distribution function is consistent with an earlier prediction of gravitational clustering, over the entire range of peculiar velocities, from field galaxies to rich clusters, on scales up to 50 Mpc (H=100). In the simplest consistent model, most of the inhomogeneous mass of the Universe is in galaxies or their halos. We estimate the ``Mach Number'' for the bulk flow within 50 Mpc (H=100) from us to be approximately 0.8, which includes the effect of high-dispersion galaxies in clusters.

28 pages, gzipped postscript file, including 11 figures and 2 tables; To appear in the Astrophysical Journal, March 1996