Dynamic monopolies in graphs have been studied as a model for spreading processes within networks. Together with their dual notion, the generalized degenerate sets, they form the immediate generalization of the classical notions of vertex covers and independent sets in a graph. We present results concerning dynamic monopolies in graphs of given average threshold values extending and generalizing previous results of Khoshkhah et al. [On dynamic monopolies of graphs: The average and strict majority thresholds, Discrete Optimization 9 (2012) 77-83] and Zaker [Generalized degeneracy, dynamic monopolies and maximum degenerate subgraphs, Discrete Appl. Math. 161 (2013) 2716-2723].