Exploring One-Variable Data

Describing Distributions

Describing a distribution's shape, center, spread, and outliers.

Intermediate20 min lesson3 min readUpdated August 12, 2026Author not yet attributed

Prerequisites

Dotplots, Histograms & Boxplots

Putting a Distribution's Shape into Words

A graph shows a distribution's shape, but a graph alone doesn't communicate it to someone who can't see it. Before reading on: what specific things would you need to describe in words to give someone an accurate mental picture of the books-read data from the previous lesson, without showing them the actual dotplot?

Definition — Describing a Distribution: Shape, Outliers, Center, Spread

A complete description names the shape (symmetric, or skewed left/right, and unimodal or bimodal), any outliers, the center (a typical or representative value), and the spread (how much the data varies) — always stated in the context of what's being measured, not just as bare numbers.

Worked Example — Describing the Books-Read Distribution

Using the previous lesson's boxplot: the distribution is right-skewed — most students read a modest number of books (mounded around 4–5), with one student's much higher count (12, a confirmed outlier) stretching the distribution's tail toward higher values. A typical student read about 4 to 5 books. The middle 50% of students span an IQR of just 2 books (4 to 6), a fairly tight cluster — but the outlier widens the full range to 10 books (2 to 12).

Worked Example — Describing and Contrasting a Second Distribution

A different group of 12 students' exam scores: 55, 70, 78, 82, 85, 88, 90, 90, 92, 94, 95, 96. Most scores cluster high, from the mid-80s to the mid-90s, with two noticeably lower scores (55, 70) stretching a tail toward lower values — this distribution is left-skewed, the mirror image of the books-read data's right skew. A typical score here is high, roughly 88 to 90, with most students scoring similarly well and only a couple of students pulling the shape's tail downward.

Tip

The direction of skew is named after the direction of the tail, not after where most of the data sits — a right-skewed distribution has its bulk on the left and a stretched-out tail reaching right, exactly as the books-read example shows.

Common Mistakes

Describing center and spread with bare numbers and no units or context, like 'the center is 5.'
A complete description states what's being measured — 'a typical student read about 5 books' — not just a number, since the number alone doesn't communicate what it represents.
Assuming skewed left and skewed right both mean roughly the same thing, just 'not symmetric.'
The two are mirror images with different implications — right-skewed means a small number of unusually high values pull the tail rightward; left-skewed means a small number of unusually low values pull it leftward, as the two contrasting examples above show.

Key Takeaways

A complete distribution description covers shape, outliers, center, and spread — always in context.
Skew direction matches the direction of the stretched-out tail, not the side where most of the data is concentrated.
Contrasting two distributions' shapes side by side sharpens the vocabulary for describing either one alone.

Summary

This closes the 'Displaying Data' topic. The next topic replaces informal, visual judgments of center and spread with precise numerical calculations.

Track your progress

← Dotplots, Histograms & Boxplots Back to Exploring One-Variable Data Measures of Center & Spread→