### Beyond AP Statistics

#### Probability Basics

#### Small Samples

#### Distributions

#### Power

### Beyond AP Statistics

#### Probability Basics

#### Small Samples

#### Distributions

#### Power

# What is a Dotplot?

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

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## 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.

## Test Your Understanding

**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.

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