The absolute maximum may be an unusually high observation that does not represent the dataset’s main pattern. Using the adjusted maximum keeps that extreme value from determining the displayed upper range. This produces a more informative summary for skewed data, while still leaving the unusually high observation visible as a potential outlier rather than silently removing it.
The upper boundary is calculated as Q3 plus 1.5 times the IQR. Any observation above this boundary is treated as a potential outlier on the high side. The adjusted maximum is selected from the observations that remain at or below the boundary, so the rule separates the dataset’s typical upper range from values that may require additional attention.
The upper fence is a calculated cutoff, whereas the adjusted maximum must be an actual observed value. The fence establishes the highest permitted boundary for the typical range, but it may not equal any measurement in the dataset. The adjusted maximum is therefore the largest recorded observation that does not exceed that calculated cutoff.
First determine Q3 and the IQR for the dataset. Next calculate the upper fence using Q3 + 1.5 IQR. Compare each observation with that boundary, exclude observations above it from the typical upper range, and select the largest remaining value. That selected observation is the adjusted maximum used in the summary.
In a box-and-whisker plot, the adjusted maximum determines the endpoint of the upper whisker. Observations beyond that endpoint can be displayed separately as potential outliers instead of extending the whisker to the absolute maximum. This visual arrangement helps viewers distinguish the distribution’s main upper range from unusually high measurements.
Adjusted maximum values allow analysts to compare the upper ranges of skewed distributions without letting one extreme observation dominate the displayed scale. When used with box-and-whisker plots, they help reveal differences in typical upper limits and make potential high-side outliers easier to distinguish across datasets.