# What is a Dotplot?

A dotplot is a type of graphic display used to compare frequency counts within categories or groups.

## Dotplot Overview

As you might guess, a dotplot is made up of dots plotted on a graph. Here is how to interpret a dotplot.

• Each dot represents a specific number of observations from a set of data. (Unless otherwise indicated, assume that each dot represents one observation. If a dot represents more than one observation, that should be explicitly noted on the plot.)
• The dots are stacked in a column over a category, so that the height of the column represents the relative or absolute frequency of observations in the category.
• The pattern of data in a dotplot can be described in terms of symmetry and skewness only if the categories are quantitative. If the categories are qualitative (as they often are), a dotplot cannot be described in those terms.

Compared to other types of graphic display, dotplots are used most often to plot frequency counts within a small number of categories, usually with small sets of data.

## Dotplot Example

Here is an example to show what a dotplot looks like and how to interpret it. Suppose 30 first graders are asked to pick their favorite color. Their choices can be summarized in a dotplot, as shown below.

 ********* ** *** ***** ******* * *** Red Orange Yellow Green Blue Indigo Violet

Each dot represents one student, and the number of dots in a column represents the number of first graders who selected the color associated with that column. For example, Red was the most popular color (selected by 9 students), followed by Blue (selected by 7 students). Selected by only 1 student, Indigo was the least popular color.

In this example, note that the category (color) is a qualitative variable; so it is not appropriate to talk about the symmetry or skewness of this dotplot. The dotplot in the next section uses a quantitative variable, so we will illustrate skewness and symmetry of dotplots in the next section.

Problem 1

The dotplot below shows the number of televisions owned by each family on a city block.

 * *** ***** **** *** ** * * * 0 1 2 3 4 5 6 7 8

Which of the following statements are true?

(A) The distribution is right-skewed with no outliers.
(B) The distribution is right-skewed with one outlier.
(C) The distribution is left-skewed with no outliers.
(D) The distribution is left-skewed with one outlier.
(E) The distribution is symmetric.

Solution

The correct answer is (A). Most of the observations are on the left side of the distribution, so the distribution is right-skewed. And none of the observations is extreme, so there are no outliers.

Note: Because the categories are quantitative (i.e., numbers), it is appropriate to describe the skewness of the data in this dotplot.