  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.
