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Social outliers draw a lot of attention from those inside and outside their group and yet little is known about their impact on perceptions of their group as a whole. The present studies examine how outliers influence observers’ summary perceptions of a group’s behavior and inferences about the group’s descriptive and prescriptive norms. Across four studies (N = 1739) we examine how observers perceive descriptive and prescriptive social norms in groups containing outliers of varying degrees. We find consistent evidence that observers overweight outlying behavior when judging the descriptive and prescriptive norms, but overweight outliers less as they become more extreme, especially in perceptions of the prescriptive norm. We find this pattern across norms pertaining to punctuality (Studies 1-2, 4) and clothing formality (Study 3) and for outliers who are both prescriptively and descriptively deviant (e.g. late arrivers), as well as for outliers who are only descriptive deviants (e.g. early arrivers). We further demonstrate that observers’ perceptions of the group shift in the direction of moderate outliers. This occurs because observers anchor on the outlier’s behavior and adjust their recollections of non-outlying individuals, making their inferences about the group’s average behavior more extreme.