Unimodal distribution

Unimodal describes the shape of a distribution, not its center and not its spread: the values pile up around one location and thin out on both sides. You judge it from a graph, a dotplot or a histogram or a stemplot, by counting the major peaks and ignoring the small ups and downs that ordinary randomness puts into the counts.

The word mode is doing two different jobs, and that is where the trouble starts. Take the eight values 3, 4, 5, 5, 6, 6, 7, 8. Counted as data, two values tie for most frequent: 5 and 6, each appearing twice. Drawn as a dotplot, the column heights read 1, 1, 2, 2, 1, 1: the picture rises to a flat top in the middle and falls away on both sides, which is one hump. Two most-frequent values, one peak, and unimodal follows the picture.

So "there are two modes, so the distribution is bimodal" is the sentence to catch. Bimodal means two clearly separated clumps with a genuine dip between them, the shape you get from a graph of adult heights that mixes men and women together. Two equally tall bars standing side by side are one peak, and a bar that happens to be one dot taller than its neighbor is not a second peak either.

Modality is a judgment about the underlying shape rather than a fact about one drawing. Narrow bins turn a smooth pile into a ragged line with several small spikes, and wide bins can flatten two real groups into one. Change the bin width, redraw, and see whether the second peak survives. A distribution with no peak at all, roughly flat across its whole range, is uniform rather than unimodal.

Unimodal says nothing about symmetry. A unimodal distribution can be symmetric, right-skewed, or left-skewed, so the two words are separate parts of the same description and you need both. Shape, center, variability, and unusual features are the four things a description names in context, and in the Fall 2026 course topic 1.6 is titled Descriptions for One Quantitative Variable Distributions.