Wiki Page, Math 13 - Perez Sandbox : Module 4 - Dotplots (2a of 2)

Wiki Page
2026-01-17T21:15:48-08:00

Describing the Distribution of a Quantitative Variable

Now we will give more specific advice on how to describe the distribution of a quantitative variable.

When we describe patterns in data, we use descriptions of shape, center, and spread. We also describe exceptions to the pattern. We call these exceptions outliers.

Describing Shape

To describe the shape of a distribution, imagine sketching the outline of the data to emphasize the general trend.

Some Common Descriptions of Shape

Right skewed: A right-skewed distribution of data has a cluster of data on the left with a tail of data tapering off to the right. So a right-skewed distribution has a lot of data at lower variable values with smaller amounts of data at higher variable values.

EXAMPLE A distribution with a right skew

The distribution of sugar in adult cereals is skewed to the right.

Left skewed: A left skewed distribution of data has a cluster of data on the right with a tail of data tapering off to the left. So a left skewed distribution has a lot of data at higher variable values with smaller amounts of data at lower variable values.

EXAMPLE A distribution with a left skew

This distribution of sugar in children's cereals is skewed to the left.

Symmetric with a central peak (also called bell-shaped): A bell-shaped distribution has a central peak with a tail in both directions. So, a bell-shaped distribution has a lot of data in the center with smaller amounts of data tapering off in each direction.

EXAMPLE Symmetric with a central peak

The distribution of calories in children’s cereals is symmetric with a central peak. It is bell-shaped. The distribution of calories in adult cereals is also roughly bell-shaped.

Uniform: Equal number data points for each variable value

A uniform distribution of data has the same amount of data for each variable value. So a uniform distribution of data has a rectangular shape.

EXAMPLE Uniform distribution of data

Here is the last digit from 47 students’ telephone numbers. The distribution of the digits is roughly uniform.

Mark this page as done, then click the "Next" or > button to continue.

Content by the Open Learning Initiative and licensed under CC BY.