Move One Value and Watch Which Summaries Flinch

You'll learnwhich summaries an extreme value can drag and which ones ignore it, by changing a single commute and recomputing all five on screen.

Twenty one-way commutes, in minutes, built so the mean and the median are both exactly 30. Then one person moves house and their commute goes from 41 minutes to 95. Nobody else's changes. The mean climbs to 32.7, the standard deviation nearly triples, the range more than triples — and the median and the interquartile range do not move at all. That single edit is the whole topic: it sorts every summary in this course into the ones a far-out value can drag and the ones it cannot, and it explains why a skewed data set is reported with a median and an IQR rather than with a mean and a standard deviation. Every number on the screen is computed from the twenty values, so a drawn shape and the card describing it cannot disagree.

8 STEPS · 6 QUICK CHECKS · MEAN vs MEDIAN · STANDARD DEVIATION · QUARTILES · IQR · OUTLIER FENCES · v1

one commute moves 41 → 95 · mean +2.7, median +0 · SD ×2.66, IQR ×1

Before you start

What you're looking at

Twenty one-way commute times in minutes: a dotplot on top, the boxplot of the same twenty underneath, and a shaded band one standard deviation either side of the mean.

The question

If one person's commute changes and nobody else's does, which summaries move — and by how much?

Watch for

The green mean rule sliding right while the white median rule stays exactly where it is, and the shaded band widening while the box does not.

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