The Fattest Region Holds Exactly as Many as the Thinnest

You'll learnhow to build a boxplot from five numbers and read it without mistaking a wide region for a crowded one, by counting what is actually in each quarter.

Twenty-four donations to a school fundraiser, drawn as a boxplot. Its four regions have widths of $8.00, $7.00, $17.50 and $32.50 — the last is four and a half times the first — and every one of them holds exactly six donations. That is the whole of what a boxplot is: five numbers drawn to scale, with a quarter of the data between each pair. A long whisker means the values out there are spread thin, never that there are more of them. This animation builds the plot move by move, counts each region rather than asserting it, retracts a whisker when one donation crosses the outlier fence, and then draws the identical boxplot over five times as much data to show what the picture does not carry. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · FIVE-NUMBER SUMMARY · QUARTERS · WHISKERS · OUTLIERS · SKEW · v2

Four regions 8, 7, 17.50 and 32.50 wide — and six donations in every one.

Before you start

What you're looking at

Twenty-four donations to a school fundraiser, in dollars: a boxplot on top and the same twenty-four as a dotplot underneath, on one shared axis.

The question

The four regions of the boxplot are wildly different sizes. How much of the data is in each one?

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