2C Box-and-whisker plots

Chapter 2 · pages 58–62 · 1313 words

A box-and-whisker plot is the picture version of the 5-number summary from section 2B. You draw a long thin box running from the lower hinge to the upper hinge, cross it with a bar marking the median, and then extend a "whisker" from each end of the box out to the corresponding extreme. In one glance you see spread (the box), center (the bar), and range (the whisker tips), laid out vertically along a measurement scale — for example, comparing the heights of the 50 states' highest points against the heights of 219 volcanoes side by side, both scaled in feet from 0 to 20,000.

   Height
   (feet)
   20,000 -                    o  <- extreme (e.g. Alaska)
            |
   15,000 -                    |
            |
   10,000 - [   ]              [====]  <- box: hinge to hinge
            [===]  <- median   [====]
   5,000  - [   ]              [====]
            |                    |
      0   -  o                   o   <- extreme
          States               Volcanoes

Because a box-and-whisker plot spends so much ink on empty space compared to just listing the five numbers, that empty space is not wasted — it is room for identification. Rather than leaving the extremes as bare dots, you can label them with the case they belong to (Alaska at the top, Delaware and Florida at the bottom, for instance), and you can identify a handful of other unusual points near the ends too. When you do this, the recommended practice is to stop the whisker at the innermost point you've bothered to identify, rather than running it all the way to the single most extreme value — the whisker then marks the identified range, not just the numerical extreme.

This section also uses box-and-whisker plots to launch a broader lesson on plotting technique. The key distinction is between what makes plotting easy and what makes a plot effective: a grid of ruled lines on ordinary graph paper helps you place points accurately but clutters the final picture and hides the pattern you're trying to see. The fix is to plot on tracing paper (or acetate) laid over a sheet of well-printed graph paper slipped underneath — you plot using the grid showing through, add your reference lines and a few scale ticks, then lift away the graph sheet so the finished plot is uncluttered. Good graph paper for this purpose has clean lines with every 10th line heavy and every 5th line medium; cheap "five and dime" or quadrille paper makes the job harder. On a finished plot only three or four scale values should be shown per axis, though while actively plotting it helps to have many more marked, and to put the horizontal scale above the plot rather than below so your hand doesn't block it. In a pinch, with no graph paper at all, you can improvise a grid by placing one sheet of ruled paper sideways beneath another sheet of ruled paper, letting the lines of the bottom sheet show through the top one.

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