# Lesson 4

The Shape of Distributions

### Lesson Narrative

The mathematical purpose of this lesson is to describe distributions using the appropriate terminology. In order to learn more about different kinds of distributions, one thing students do is invent reasonable contexts for a given distribution. The terminology that is used is described here.

• In a symmetric distribution, the mean is equal to the median and there is a vertical line of symmetry in the center of the data display.
• In a skewed distribution, the mean is not usually equal to the median and one side of the distribution has more values farther from the bulk of the data than the other side.
• A uniform distribution has the data values evenly distributed throughout the range of the data.
• A bimodal distribution has two very common data values seen in a dot plot or histogram as distinct peaks.
• A bell-shaped distribution has a dot plot that takes the form of a bell with most of the data clustered near the center and fewer points farther from the center.

In grade 6, students may have acquired some different ways to describe distributions, though they weren’t required to learn the terminology introduced in this lesson. In a previous lesson, students created data displays. In upcoming work, students will use information about the shape of distributions to determine the appropriate measure of center. The Which One Doesn’t Belong activity gives students a reason to begin using language precisely (MP6) and gives the teacher the opportunity to hear how they use terminology and talk about characteristics of the items in comparison to one another. In the card sort, students trade roles explaining their thinking and listening, providing opportunities to explain their reasoning and critique the reasoning of others (MP3).

### Learning Goals

Teacher Facing

• Describe (orally and in writing) the shape of a distribution using words such as "symmetric, skewed, uniform, bimodal, and bell-shaped."
• Interpret a graphical representation to suggest a possible context for the data.

### Student Facing

• Let’s explore data and describe distributions.

### Required Preparation

Print and cut up slips from the blackline master. Prepare one copy for every two students.

### Student Facing

• I can describe the shape of a distribution using the terms "symmetric, skewed, uniform, bimodal, and bell-shaped."
• I can use a graphical representation of data to suggest a situation that produced the data pictured.

Building Towards

### Glossary Entries

• bell-shaped distribution

A distribution whose dot plot or histogram takes the form of a bell with most of the data clustered near the center and fewer points farther from the center.

• bimodal distribution

A distribution with two very common data values seen in a dot plot or histogram as distinct peaks. In the dot plot shown, the two common data values are 2 and 7,

• skewed distribution

A distribution where one side of the distribution has more values farther from the bulk of the data than the other side, so that the mean is not equal to the median. In the dot plot shown, the data values on the left, such as 1, 2, and 3, are further from the bulk of the data than the data values on the right.

• symmetric distribution

A distribution with a vertical line of symmetry in the center of the graphical representation, so that the mean is equal to the median. In the dot plot shown, the distribution is symmetric about the data value 5.