We perform an experiment designed to assess the accuracy of beliefs about distributions. The beliefs relate to behavior (mobile phone purchasing decisions, hypothetical restaurant choices), attitudes (happiness, politics) and observable characteristics (height, weight) and are typically formed through real world experiences. We find a powerful and ubiquitous bias in perceptions that is “self-centered” in the sense that an individual’s beliefs about the population distribution changes with their own position in the distribution. In particular, those at extremes tend to perceive themselves as closer to the middle of the distribution than is the case. We discuss possible explanations for this bias.