Aims: The MOJAVE (MOnitoring of Jets in AGN with VLBA Experiments) survey contains 101 quasars with a total of 354 observed radio components that are different from the radio cores, among which 95% move with apparent projected superluminal velocities with respect to the core, and 45% have projected velocities larger than 10c (with a maximum velocity 60c). We try to determine whether this distribution is statistically probable, and we make an independent measure of the kinetic power required in the quasars to produce such powerful ejections. Methods: Doppler boosting effects are analyzed to determine the statistics of the superluminal motions. We integrate over all possible values of the Lorentz factor, the values of the kinetic energy corresponding to each component. The calculation of the mass in the ejection is carried out by assuming the minimum energy state, i.e., that the magnetic field and particle energy distributions are arranged in the most efficient way to produce the observed synchrotron emission. This kinetic energy is multiplied by the frequency at which the portions of the jet fluid identified as "blobs" are produced. Hence, we estimate the average total power released by the quasars in the form of kinetic energy in the long term on pc-scales. Results: A selection effect in which both the core and the blobs of the quasar are affected by huge Doppler-boosting enhancement increases the probability of finding a jet ejected within 10 degrees of the line of sight ≳ 40 times above what one would expect for a random distribution of ejection, which explains the ratios of the very high projected velocities given above. The average total kinetic power of each MOJAVE quasar should be very high to obtain this distribution: ~ 7 × 1047 erg/s. This amount is much higher than previous estimates of kinetic power on kpc-scales based on the analysis of cavities in X-ray gas or radio lobes in samples of objects of much lower radio luminosity but similar black hole masses. The kinetic power is a significant portion of the Eddington luminosity, on the order of the bolometric luminosity, and proportional on average to L0.5rad standing for radio luminosity, although this correlation might be induced by Malmquist-like bias.