In this paper we voice concerns about the uncritical manner in which the mean is often used as a summary statistic in psychological research. We identify a number of implicit assumptions underlying the use of the mean and argue that the fragility of these assumptions should be more carefully considered. We examine some of the ways in which the potential violation of these assumptions can lead us into significant theoretical and methodological error. Illustrations of alternative models of research already extant within Psychology are used to explore methods of research less mean-dependent and suggest that a critical assessment of the assumptions underlying its use in research play a more explicit role in the process of study design and review.