The Pile Is on the Left, So the Skew Is to the Right

You'll learnto read a dotplot, stemplot and histogram of one quantitative variable, to see how bin width changes what the picture says, and to name skew by the tail rather than by the pile.

Forty commutes, in minutes. Drawn as a dotplot every value is still there; as a stemplot they are still there, rearranged; as a histogram they are gone and only counts remain. Then the choice nobody warns you about: bin width. The same forty numbers give seventeen spiky bins with a real gap inside them at width 5, two clear mounds at width 10, and at width 30 a single smooth slope in which the second cluster has disappeared entirely. None of those pictures is wrong. Finally the naming that gets reversed more than any other in this course — the mound sits at the low end and the long thin stretch reaches toward 88, so this distribution is skewed RIGHT, and the mean sitting 7.65 minutes above the median is the arithmetic saying so.

8 STEPS · 6 QUICK CHECKS · DOTPLOT · STEMPLOT · HISTOGRAM · BIN WIDTH · SKEW BY THE TAIL · v1

40 commutes · widths 5, 10 and 30 · mean 33.65 vs median 26

Before you start

What you're looking at

40 people's commutes in minutes, on one number line. Most are short; a few are very long.

The question

Which display keeps the data, which throws it away — and which way is this distribution skewed?

Watch for

The empty bin inside the data at width 5, the second cluster vanishing at width 30, and the mean sitting above the median.

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