Predictions for the apparent velocity statistics under simple beaming models are presented and compared to the observations. The potential applications for tests of unification models and for cosmology (source counts, measurements of the Hubble constant H-0 and the deceleration parameter q(0)) are discussed, First results from a large homogeneous survey are presented. The data do not show compelling evidence for the existence of intrinsically different populations of galaxies, BL Lacertae objects, or quasars. Apparent velocities beta(app) in the range 1-5 h(-1), where h = H-0/100 km . s(-1). Mpc(-1) [1 megaparsec (Mpc) = 3.09 x 10(22) m], occur with roughly equal frequency; higher values, up to beta(app) = 10 h(-1), are rather more scarce than appeared to be the case from earlier work, which evidently concentrated on sources that are not representative of the general population. The beta(app) distribution suggests that there might be a skewed distribution of Lorentz factors over the sample, with a peak at gamma(b) approximate to 2 h(-1) and a tail up to at least gamma(b) approximate to 10 h(-1). There appears to be a clearly rising upper envelope to the beta(app) distribution when plotted as a function of observed 5-GHz luminosity; a combination of source counts and the apparent velocity statistics in a larger sample could provide much insight into the properties of radio jet sources.