Comparative dotplot

A comparative dotplot stacks two or more dotplots above a single shared scale. Every dot is still one observation sitting at its own value, so nothing is summarized away: repeats, gaps and clusters all survive into the picture. The shared scale is the requirement. Two dotplots drawn on different axes cannot be compared by eye no matter how they are arranged.

Two groups of nine make the point. Group A is 11, 12, 12, 13, 14, 15, 16, 16, 17 and group B is 11, 12, 12, 12, 14, 16, 16, 16, 17. Both have mean 14, median 14, and the same five-number summary of 11, 12, 14, 16 and 17 under the median-excluded (TI-84) rule this site uses, so their boxplots are identical. The dotplots are not. A puts a dot at every value from 11 to 17, while B piles three dots on 12, three on 16, and leaves 13 and 15 empty.

The error to name is reading height as center: "group B's tallest stack is at 12, so B is centered near 12." A stack height counts repeats, which makes it the mode. The center is a position in the ordered data, and B's median and mean are both 14, a value carrying a single dot. In a set with two clumps, the tallest stack can sit a long way from every measure of center.

The display fails as $n$ grows, because stacks of forty dots stop being countable and start being bars, at which point a histogram is the honest choice. If the groups differ in size, read each stack as a share of its own group rather than as a raw count.

Topic 1.9 of the Fall 2026 course names dotplots among the displays for comparing distributions, specifically because they show clusters and gaps that boxplots cannot.