Outliers and What They Do

The big idea

An outlier is a value unusually far from the rest, and Math 1 has a rule for it: find the IQR, multiply by 1.5, and build two fences, Q1 minus that amount and Q3 plus it. Any value past a fence is an outlier, and a modified box plot shows it as its own dot with the whisker stopping at the last value inside the fences. Outliers pull the mean and the standard deviation, because both use every value's size, and a far value's distance gets squared into the standard deviation. The median and the IQR resist, because they use only the order. When the 74 inch player joins the team the mean and standard deviation rise and the median and IQR hold still, so the median describes a typical player; the 100 minute class period does the same thing to the class periods. That is why skewed data or data with outliers is described with the median and the IQR. And an outlier is never simply deleted: ask whether it is a mistake to fix or a real value to keep.