Lesson 2
Data Representations
Lesson Narrative
This lesson is optional because it revisits below gradelevel content. If the preunit diagnostic assessment indicates that your students know the representations well, this lesson may be safely skipped.
In grade 6, students displayed numerical data in plots on a number line, including dot plots, histograms, and box plots. This lesson serves as a brief review of the meaning of these representations and how they are created.
In this lesson, students represent data using histograms and box plots. They calculate values for the fivenumber summary and use those values to create dot plots. Students will also create two different histograms that represent the same data set by using different intervals in each of the histograms. Students will also compare a dot plot, box plot, and histogram that represent the same data set. When students identify the information displayed by different graphical representations they are building knowledge about when to use appropriate tools so that they can make choices about how to represent data.
Students make use of structure (MP7) to connect visual representations of data sets and students reason abstractly and quantiatively (MP2) by interpreting values in the given contexts.
Learning Goals
Teacher Facing
 Create a dot plot, histogram, and box plot to represent numerical data.
 Identify (in writing) the fivenumber summary that describes given statistical data.
 Interpret a box plot that represents a data set.
Student Facing
 Let’s represent and analyze data using dot plots, histograms, and box plots.
Learning Targets
Student Facing
 I can find the fivenumber summary for data.
 I can use a dot plot, histogram, or box plot to represent data.
CCSS Standards
Glossary Entries

categorical data
Categorical data are data where the values are categories. For example, the breeds of 10 different dogs are categorical data. Another example is the colors of 100 different flowers.

distribution
For a numerical or categorical data set, the distribution tells you how many of each value or each category there are in the data set.

fivenumber summary
The fivenumber summary of a data set consists of the minimum, the three quartiles, and the maximum. It is often indicated by a box plot like the one shown, where the minimum is 2, the three quartiles are 4, 4.5, and 6.5, and the maximum is 9.

nonstatistical question
A nonstatistical question is a question which can be answered by a specific measurement or procedure where no variability is anticipated, for example:
 How high is that building?
 If I run at 2 meters per second, how long will it take me to run 100 meters?

numerical data
Numerical data, also called measurement or quantitative data, are data where the values are numbers, measurements, or quantities. For example, the weights of 10 different dogs are numerical data.

statistical question
A statistical question is a question that can only be answered by using data and where we expect the data to have variability, for example:
 Who is the most popular musical artist at your school?
 When do students in your class typically eat dinner?
 Which classroom in your school has the most books?