Outlier Upper Fence

The upper fence is the mirror of the lower one: Q₃ plus one and a half interquartile ranges. With Q₃ = 72 and IQR = 24 it lands at 72 + 36 = 108, so any observation above 108 is drawn as a separate point outside the whisker. Because it is built from quartiles rather than the mean and standard deviation, the rule cannot be sabotaged by the very outliers it is looking for — a mean-and-σ rule inflates σ when an extreme value is present and can end up hiding it, a failure known as masking.

Real-world skew is the thing to watch. Right-skewed data — salaries, insurance claims, download sizes — routinely put several percent of observations above the upper fence with nothing wrong at all, so a box plot of claims that shows a dozen high dots is describing the business, not finding errors. In practice the upper fence earns its keep as a screening tool: in laboratory quality control it flags samples for a re-run rather than for deletion. Solving backwards is handy when reading someone else's plot — a whisker ending at 100 above a box top of 70 implies IQR = 30/1.5 = 20.