Statistics of the stress drops associated with the Portevin-Le Châtelier effect in an Al-Mg alloy were studied both experimentally and theoretically. It was shown that the character of the statistics changes from a peaked distribution of the stress drop magnitudes to a monotonically decreasing one as the imposed strain rate or the temperature are increased. A discrete model based on a micromechanically founded local constitutive equation combined with spatial coupling between the elements of the system was shown to reproduce the observed statistical behaviour. The mechanism of spatial coupling is connected with elastic stresses due to local plastic incompatibilities. The model was further applied to simulate spatial deformation patterns including propagative deformation bands. The systematics of the bands reported in the literature as well as the observed dependence of the band velocity on the imposed deformation rate were recovered. It was concluded that the model proposed provides an adequate description of both the statistics of stress discontinuities and the spatial features of the Portevin-Le Châtelier effect.