Yang Wang¹ (), Timothy F Brady¹, Sarah H Kerns³, Jeremy B Wilmer²; ¹UCSD, ²Wellesley College, ³Dartmouth College

Data visualizations commonly use averages to enhance interpretability, but this may not always lead to accurate comprehension. Ensemble processing—the human ability to perceive summary statistics from groups of objects—is effective in various domains, yet its role in graph interpretation is underexplored. This study examines how individuals interpret averages using different graphical representations. We tested 157 UCSD undergraduate students across four conditions. In the 'explicit mean' conditions, bar graphs and dot plots explicitly displayed the average, omitting raw data. In the 'individual data' conditions, cloud plots and sinaplots depicted individual data points without explicitly indicating the mean. Surprisingly, the bar graph condition resulted in the least accurate average estimations. Despite clear labels and instructions, many participants misinterpreted the bar's height, often assuming the midpoint represented the average instead of the top edge. This aligns with the "Bar-Tip Limit" error, where viewers mistakenly perceive the bar's tip as the data's outer limit. Dot plots yielded more accurate average estimations, providing clearer guidance on average values, though this precision may impart a false sense of certainty by failing to convey the natural variability in the data. In the 'individual data' conditions, participants effectively estimated averages in cloud plots and sinaplots for normally distributed data, with variability reflecting natural uncertainty. For skewed distributions, estimates were somewhat less accurate, showing a bias toward the median. These findings suggest that visualizing individual data points leverages ensemble perception abilities, enabling viewers to extract meaningful averages while preserving data variability. Overall, the study shows that bar graphs are prone to misinterpretation when representing averages, whereas dot plots offer clearer guidance. More importantly, visualizing individual data points, as in cloud plots and sinaplots, appears superior for conveying meaningful averages with inherent data uncertainty, emphasizing the need to select appropriate graphical representations for effective data interpretation.