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 bellshaped 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 bellshaped."
 Interpret a graphical representation to suggest a possible context for the data.
Student Facing
 Let’s explore data and describe distributions.
Required Materials
Required Preparation
Print and cut up slips from the blackline master. Prepare one copy for every two students.
Learning Targets
Student Facing
 I can describe the shape of a distribution using the terms "symmetric, skewed, uniform, bimodal, and bellshaped."
 I can use a graphical representation of data to suggest a situation that produced the data pictured.
CCSS Standards
Glossary Entries

bellshaped 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.

uniform distribution
A distribution which has the data values evenly distributed throughout the range of the data.
Print Formatted Materials
Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.
Student Task Statements  docx  
Cumulative Practice Problem Set  docx  
Cool Down  Log In  
Teacher Guide  Log In  
Teacher Presentation Materials  docx  
Blackline Masters  zip 