Jeremy B Wilmer¹, Tugral Bek Awrang Zeb¹, Sarah H Kerns^1,2, Ken Nakayama³; ¹Wellesley College, ²Dartmouth College, ³University of California at Berkeley

A common graphing practice in science, health, education, and media is to focus on a single summary statistic, such as the average (mean) value. By hiding the variability in the raw data, a graphed average provides a single, salient reference point for comparison; a benchmark against which individual values, or other average values, may be compared. While known to be an over-simplification, such simplicity is deemed necessary for clear visual communication, especially to a general audience (Kerns & Wilmer, 2021). It is common practice, for example, in standardized test score reports, such as the one for the statewide K-12 Massachusetts Comprehensive Assessment System (MCAS), to provide the average score as a reference point. Yet could a single benchmark be over-interpreted? Potentially, a salient average value could polarize people’s sentiments about scores. Rather than interpret the average correctly as merely the center of a spectrum, people might interpret it, without nuance, as a categorical boundary that artificially splits scores into two types: above average (good) and below average (bad). Here, we show that this is indeed the case. When asked to rate how happy one would be to receive various potential scores, shown relative to an average value, people’s ratings are strongly polarized, with a disproportionate change when crossing the average score, relative to identical increments that do not cross the average. We next demonstrate a powerful, complete solution: show the data. When a full spectrum of individual values is graphed in place of the mean, polarization vanishes. We replicate both presence and removal of polarization across eight different practical domains, ranging from education to health to life skills. We conclude that graphed average values unnecessarily fuel polarized sentiment, and that an effective, actionable solution is to plot individual values.

Acknowledgements: Funded in part by NSF award #1624891 to JBW, a Brachman Hoffman grant to JBW, and a subaward from NSF grant #1837731 to JBW.