A random process and highly accurate pseudospectral method associated with compact finite differences are incorporated to evaluate effects of permeability heterogeneity to gravity-driven miscible porous media flows. Flows in heterogeneous permeability fields, based on multiple sets of random realizations with identical statistical characteristics, are simulated to elucidate the global trend of mean quantities and local variations. The presence of heterogeneity provokes more prominent fingering competition and greater variation of fingers' widths, hence the mean values of interested quantitative measures, i.e., breakthrough time, amount of fluid volumes transported, and normalized mixing effectiveness, are generally reduced. Resonant effects, whose influences on the flow fields are the most significant, are verified to occur in an intermediate correlation length, in which the widths of fingers are slightly less than the correspondent correlation length. Nevertheless, under the resonant conditions these measures are the most widely scattered between different random realizations associated with the same control parameters. The widest scatterings are mainly because of the enhancing sensitivity of flow path selections under such resonant conditions, especially in a few realizations whose high or low permeability regions align along with or transverse to the main flow direction. The significant scatterings of these quantitative measures, which had drawn little attention previously, suggest more cautious treatments for practical implementations in the regime of resonant effects.