# 1.5 Shape of a Distribution

A histogram shows the shape of the distribution of a quantitative variable. The shape of a distribution includes the following three aspects:

- Overall shape: what the distribution looks like, e.g., bell-shaped, J-shaped, triangular, and uniform. (See examples in the figures below.)
- Modality: number of peaks (highest points). A distribution is called
**unimodal**if it has only one peak,**bimodal**if it has two peaks, and multimodal if it has more than two peaks. - Symmetry and skewness. If you fold a distribution in the middle and the two parts can match, the distribution is called
**symmetric**. If it has a longer left tail, it is called skewed to the left (or left skewed), and skewed to the right (or right skewed) if it has a longer right tail.

The following figure shows some special shapes of distributions.

Distributions in Figure 1.8 can be described respectively as follows:

(a) bell-shaped, unimodal, and symmetric

(b) triangular, unimodal, and symmetric

(c) rectangular, no peak, and symmetric

(d) unimodal and right-skewed

(e) unimodal and left-skewed

(f) J-shaped, unimodal, and left skewed

(g) reversed J-shaped, unimodal, and right-skewed

(h) bimodal and symmetric

(i) multimodal and asymmetric

Example: Shape of a Distribution

Comment on the overall shape and modality of the following histogram.

Figure 1.8.1: The histogram of the grades data above shows its distribution is bell-shaped, unimodal, and symmetric. [Image Description (See Appendix D Figure 1.8.1)]