Show the distribution when readers must judge values around a mean

Show the underlying distribution when readers need to judge what values may plausibly occur around a mean. For example, when a chart would otherwise show only an average as a rising or falling bar, replace that mean bar with a depiction of the distribution itself instead of making readers infer likely values from the filled bar.

The within-the-bar bias appears because the bar creates a closed region on only one side of the mean. A distribution display makes the relevant data structure explicit instead of letting the filled bar imply that one side of the mean contains the data.

Mechanism: Showing the distribution removes the misleading cue that values inside the bar are more likely than equally distant values outside it.

Evidence: Viewers consistently favored within-bar values over equally distant outside-bar values when reasoning about whether a value belonged to the underlying distribution, and this bias was strong enough to reverse decisions when the same mean was shown with rising versus falling bars (Newman & Scholl, 2012).

• User Goal: Judge which values around a mean are plausible, or make a decision based on that judgment.
• Task: Interpret the distribution around a mean rather than only the mean itself.
• Data: Quantitative observations that can lie above and below the mean.
• Chart Setting: The current design shows only a mean as a bar, with or without error bars, and the chart may remain visible during judgment.
• Audience: Readers are making an interpretation or decision from the chart rather than only reading off the average.
• Success Criterion: Decisions do not flip simply because one side of the mean lies inside a filled bar.

Break it when: You cannot show the underlying distribution and only need to report the mean itself. Why: The source recommends using a point for the mean rather than an asymmetric bar in that case.

Sacrifice: You move away from a summary-only mean display to a fuller depiction of the data. Risk: Forcing this rule when a distribution display is not possible can block a simpler mean report. Mitigation: If you cannot show the distribution, fall back to a point mark for the mean rather than a bar.

Mistake: Keep the mean bar and add uncertainty decoration instead of exposing the distribution. Why it fails: The within-the-bar bias remained with error bars and during free viewing.

Failure Sign: A recommendation to increase versus decrease a value would reverse if the same mean were redrawn as a rising bar versus a falling bar. Quick Check: Mock the same mean once from a lower axis and once from an upper axis; if the two versions suggest different plausible directions, the summary bar is distorting interpretation. Stronger Test: Ask whether equally distant positive and negative values around the mean seem equally likely while the chart is visible.

• Replace the mean bar with a depiction of the underlying distribution.
• Remove the asymmetric filled bar if it is the only cue to the summarized result.
• If a full distribution display is not possible, replace the bar with a point mark for the mean.