In this paper, we consider the problem of privacy preservation in the average consensus problem when communication among nodes is quantized. More specifically, we consider a setting where nodes in the network can be curious, while certain nodes in the network want to ensure that their initial states cannot be inferred exactly by these curious nodes. Curious nodes are not malicious, i.e., they try to identify the initial states of other nodes based on the data they receive during their operation (and some of them might even collude) but do not interfere in the computation in any other way. Each node in the network (including curious nodes) can opt to execute a privacy-preserving algorithm (so as not to reveal the initial state it contributes to the average calculation) or its underlying (plain) average consensus algorithm (if privacy is not a concern). We propose two privacy-preserving event-triggered quantized average consensus algorithms. Under certain topological conditions, both proposed algorithms allow the nodes who adopt privacy-preserving protocols to preserve their privacy and at the same time to obtain, after a finite number of steps, the exact average of the initial states while processing and transmitting <italic>quantized</italic> information. We also present illustrative examples and comparisons of our algorithms against other algorithms in the existing literature, and discuss a motivating application in which smart meters in a smart grid collect real-time demands in a privacy-preserving manner.