Using stacking of images obtained at different epochs, we studied the variability properties of linear polarization of active galactic nucleus (AGN) jets on parsec-scales. Our sample is drawn from the MOJAVE programme, and consists of 436 AGNs manifesting core-jet morphology and having at least five VLBA observing epochs at 15 GHz from 1996 January through 2019 August, with some additional archival VLBA data reduced by us. We employed a stacking procedure and constructed maps of (i) standard deviation of fractional polarization and electric vector position angle (EVPA) over epochs as the measure of variability and (ii) median polarization degree to quantify typical values in time. The distributions of these values along and across the jet were analysed for the whole sample for the first time. We found that core EVPA variability is typically higher than that of the jet, presumably due to component blending and outflow bends in the core. The BL Lacertae object cores have lower EVPA variability, compared to that of quasars, possibly due to lower Faraday rotation measure, suggesting a stronger ordered magnetic field component. The EVPA becomes more stable down the jet. Most of the sources showing this trend have a time coverage of more than 12 yr and at least 15 epochs. The possible cause could be the increase of stability in the magnetic field direction, reflecting an increase in the fraction of the magnetic field that is ordered. There are no significant optical-class-dependent or spectral-class-dependent relations in the EVPA variability properties in AGN jets.