Side-by-side boxplot

A side-by-side boxplot puts one boxplot per group on a single common axis. Each box runs from $Q_1$ (the first quartile) to $Q_3$ (the third quartile) with the median marked inside, and each of the four sections, two whiskers and two halves of the box, covers about a quarter of that group's values. This site takes quartiles by the median-excluded (TI-84) rule.

Eleven commute times for group A are 20, 22, 24, 25, 26, 28, 30, 33, 38, 45 and 52 minutes, giving a five-number summary of 20, 24, 28, 38 and 52 and an $\text{IQR}$ of $38 - 24 = 14$. Group B's eleven times are 26, 28, 29, 30, 31, 32, 33, 34, 35, 36 and 40, summarizing to 26, 29, 32, 35 and 40 with an $\text{IQR}$ of 6. Read side by side: B's median sits 4 minutes higher and B is less than half as variable.

The misreading is about length: "A's upper whisker is far longer than its lower one, so most of A's data is at the high end." Length is spread, not count. A's lower whisker runs 20 to 24, four minutes, and the upper runs 38 to 52, fourteen minutes, but each of them covers about a quarter of the eleven values. The long upper whisker says the top quarter is stretched thin, which is the signature of right skew, and no more than that.

Five numbers per group is all a boxplot carries, so it cannot show a cluster, a gap, or a second peak. When shape matters, put a comparative dotplot next to it. Overlapping boxes are also not a test: separation on a graph is not a significance decision.

Topic 1.9 of the Fall 2026 course puts it plainly. Boxplots compare center, variability, outliers, and skew or symmetry, but they do not show clusters or gaps.