Context. Blue-shifted Fe K absorption lines have been detected in recent years between 7 and 10 keV in the X-ray spectra of several radio-quiet AGNs. The derived blue-shifted velocities of the lines can often reach mildly relativistic values, up to 0.2-0.4c. These findings are important because they suggest the presence of a previously unknown massive and highly ionized absorbing material outflowing from their nuclei, possibly connected with accretion disk winds/outflows. Aims. The scope of the present work is to statistically quantify the parameters and incidence of the blue-shifted Fe K absorption lines through a uniform analysis on a large sample of radio-quiet AGNs. This allows us to assess their global detection significance and to overcome any possible publication bias. Methods. We performed a blind search for narrow absorption features at energies greater than 6.4 keV in a sample of 42 radio-quiet AGNs observed with XMM-Newton. A simple uniform model composed by an absorbed power-law plus Gaussian emission and absorption lines provided a good fit for all the data sets. We derived the absorption lines parameters and calculated their detailed detection significance making use of the classical F-test and extensive Monte Carlo simulations. Results. We detect 36 narrow absorption lines on a total of 101 XMM-Newton EPIC pn observations. The number of absorption lines at rest-frame energies higher than 7 keV is 22. Their global probability to be generated by random fluctuations is very low, less than 3 × 10 −8 , and their detection have been independently confirmed by a spectral analysis of the MOS data, with associated random probability <10 −7 . We identify the lines as Fe XXV and Fe XXVI K-shell resonant absorption. They are systematically blue-shifted, with a velocity distribution ranging from zero up to ∼0.3c, with a peak and mean value at ∼0.1c. We detect variability of the lines on both EWs and blue-shifted velocities among different XMM-Newton observations even on time-scales as short as a few days, possibly suggesting somewhat compact absorbers. Moreover, we find no significant correlation between the cosmological red-shifts of the sources and the lines blue-shifted velocities, ruling out any systematic contamination by local absorption. If we define ultra-fast outflows (UFOs) those highly ionized absorbers with outflow velocities higher than 10 4 km s −1 , then the majority of the lines are consistent with being associated to UFOs and the fraction of objects with detected UFOs in the whole sample is at least ∼35%. This fraction is similar for type 1 and type 2 sources. The global covering fraction of the absorbers is consequently estimated to be in the range C ∼ 0.4−0.6, thereby implying large opening angles. Conclusions. From our systematic X-ray spectral analysis on a large sample of radio-quiet AGNs we have been able to clearly assess the global veracity of the blue-shifted Fe K absorption lines at E > 7 keV and to overcome their publication bias. These lines indicate that UFOs are a rather ...