We consider distributed average consensus in a wireless network with partial communication to reduce the number of transmissions in every iteration/round. Considering the broadcast nature of wireless channels, we propose a probabilistic approach that schedules a subset of nodes for broadcasting information to their neighbors in every round. We compare several heuristic methods for assigning the node broadcast probabilities under a fixed number of transmissions per round. Furthermore, we introduce a pre-compensation method to correct the bias between the consensus value and the average of the initial values, and suggest possible extensions for our design. Our results are particularly relevant for developing communication-efficient consensus protocols in a wireless environment with limited frequency/time resources.