Dotplot vs Comparative Dotplot

A dotplot puts one dot on a number line for every observation, at that observation's value, and stacks dots when values repeat. The horizontal axis is the variable's scale. The vertical direction is a count, not a second variable. Nothing is grouped and nothing is averaged, so the display loses no information: the whole data set can be read back off it.

Twelve students report how many siblings they have. Four say 0, five say 1, two say 2, and one says 3, so the plot shows stacks of height 4, 5, 2 and 1 above the marks 0, 1, 2 and 3. The mean is $\frac{0(4) + 1(5) + 2(2) + 3(1)}{12} = \frac{12}{12} = 1$ sibling. With $n = 12$ the median falls between the 6th and 7th values, both of which are 1, so the median is 1 as well.

The error that follows is reading the axis instead of the dots: "the values are 0, 1, 2 and 3, so the mean is $(0 + 1 + 2 + 3)/4 = 1.5$." That averages four axis labels. Each dot is one student, so every value has to be counted as many times as it has dots above it. The marks on the axis record which values occurred, not how often.

A dotplot conceals almost nothing, which is also where it breaks. With 400 measurements recorded to two decimals, nearly every value is unique, so you get 400 stacks one dot tall and no readable shape. That is the point at which you bin into a histogram and accept the loss. A dotplot also needs a number line, so it is the wrong display for a categorical variable.

For contrast, the five-number summary of those twelve counts is 0, 0, 1, 1.5, 3, and a boxplot drawn from it cannot show that the tallest stack sits at 1. Dotplots are one of the three displays in topic 1.5, Graphical Representations for One Quantitative Variable.

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.