Previous research suggests that sets of similar items are represented using a rapid averaging mechanism that automatically extracts statistical properties within 50 ms. However, typically in these studies, displays are not masked, so it is possible that the sets are available for longer than this duration. In the present study, using masked displays, we (a) tested a newly proposed strategy for extracting the mean size of a set of circles, and (b) more precisely evaluated the time course of rapid averaging. The results indicate that when viewing conditions are poor, performance can be explained by assuming that observers rely on information from previous trials. In this study, observers required at least a 200-ms exposure time in order to derive the average size of a set of circles without relying on information from previously-viewed sets, suggesting that rapid averaging is not as fast as previously assumed and, therefore, that it may not be an automatic process.