The Paradox of Certainty: When Graphed Ensembles Convey Averages Better than Graphed Averages

Despite the ubiquity of averages in data visualizations, theyoften lead to systematic misinterpretations, such as the "bartip-limit error," where viewers mistakenly infer the top of a baras the upper bound rather than the mean. We examined whethervisualizing raw data improves average estimation byleveraging ensemble perception—the human ability to extractstatistical summaries from multiple elements. In a withinsubjectsstudy, participants judged averages across bar plots,line plots, cloud plots, sinaplots, and hybrid "bar + cloud" plots.Results show that while bar and line plots explicitly markaverages, they frequently induce systematic errors. In contrast,cloud and sinaplots do not guarantee more precise meanjudgments but provide essential distributional context,reducing errors associated with bar and line plots. Our findingschallenge the assumption that explicit averages alone ensureaccurate interpretation and emphasize the necessity ofvisualizing raw data to mitigate errors.