  We measure the distribution of velocity dispersions of groups of galaxies
identified in the UZC catalog; we use the distribution to derive the group mass
function. We introduce a new method which makes efficient use of the entire
magnitude limited catalog. Our determination of \nst includes a significant
contribution from low luminosity systems that would be missing in a volume
limited sample. We start from a model for the probability density function of
the total number of group members and reproduce the observed distribution. We
take several effects like the local fluctuations in volume density, limited
sampling and group selection into account. We estimate the relation between
total number of members, total luminosity and true velocity dispersion. We can
then reproduce not only the observed distribution of \sv but also the
distributions of the number of group members, the total groups luminosity, and
virial mass. The best fit to the data in the true velocity dispersion range 100
km/s < \sigma < 750 km/s is a power law model with a slope -3.4 and a
normalization (1.27 +/- 0.21) x 10^{-5} h^3 Mpc^{-3}. The predictions of CDM
models are consistent with the mass function we derive from this distribution
of velocity dispersions.
