# Representing Bivariate Data Sets

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## Objective

SWBAT select an appropriate graph for a bivariate data set by assessing whether the variables are quantitative or categorical.

#### Big Idea

To create a graphical representation of a data set, we first consider whether the variables are categorical or quantitative. The type of display must be appropriate for the variable type!

## Warm-Up

15 minutes

To understand the day's lesson, my students must recall the difference between a quantitative and categorical variable.  As a fun way to refresh their memories about this, we play a quick game of Kahoot!.  This type of quiz game is very easy to make and students can access it quickly from any device that is connected to the internet.  The Kahoot! game Categorical vs. Quantitative asks students to determine whether various variables are categorical and quantitative.  To play this game, you will need to project your screen for the class to see and each student must have a connection to the internet.  Although you can play my game without an account, you will need to set up an account if you want to adapt my game or make your own.  More information about this can be found in the the document Playing Kahoot!.

## Direct Instruction

20 minutes

After the Kahoot! game, we look at the posters from the previous unit presentations, which are hanging on the wall.  These posters include a mix of one-variable and two-variable distributions. As we review the displays, I remind my students that our study of statistics has been divided into two parts:

• one-variable (univariate) statistics
• two-variable (bivariate) statistics

I ask students to point out which of the presentations involved a single variable and which ones involved two variables.  I remind them that our initial study of statistics focused on one-variable statistics.

To begin our study of bivariate statistics, we direct our attention to two –variable displays on the posters.  I point out that some relationships between two variables can be represented with a scatter plot and some cannot.  Specifically, when both of the variables are quantitative, we can use a scatter plot to investigate their relationship.  If one of the variables is categorical, though, we cannot.

Using the distributions on the posters, I ask students to classify the two variables in each display.  The following might be some examples:

• A student made a back-to-back stem plot of hand dominance and height.  This is an example of one categorical and one quantitative variable.
• Another student made a scatter plot of number of siblings and number of days since eating fast food.  This is an example of two quantitative variables.

We discuss and take notes on methods of displaying relationships between two variables.

## Data Display Activity

40 minutes

In order to help them differentiate among two variable data displays with various combinations of categorical and quantitative variables, I ask my students to complete a matching activity.  Working in pairs that I determine in advance, students use Data Display Matching Activity to practice identifying variable types.

My students have learned how to make stacked bar graphs, pie charts, parallel box plots and scatter plots in previous grades, but their work has focused on the mechanics of making the graphs.  I generally find that they need practice and instruction in choosing an appropriate graphical and describing a relationship between two variables in a display.

As with my other activities involving cards, I like to print out the Data Display Matching Activity cards on colored card stock in advance and cut them out.  This way I can use them with many classes and I don't have to waste instructional time on having kids cut out cards.  Printing each set on a different color of card stock makes it easy to keep the sets separate.

To complete the activity, each group of students will need a set of the cards and the Data Display Matching Response Sheet.  I ask students to first sort the display cards according to type of graph (box plot, scatter plot, etc).  I then ask them to match each display card (which contains a one, two, or three variable data display) with a description card (which states the number and type of variables).  When they have completed this step, they record their matches on the first page of the  response sheet.  Next, they answer questions about what the two variable displays show about the relationship between the two variables.

When students have completed this activity, they submit the  response sheet to me for grading.  In assessing this work, I look for evidence that they can interpret a relationship between two variables shown graphically [MP2].  Using my smart phone, I take pictures of some answers I like so that in the next day's lesson I can provide my students of examples of correct interpretations of two-variable data sets.

## Close of Lesson

10 minutes

To wrap up our discussion of choosing appropriate data displays, we play another quick game of Kahoot.  The 10 questions in Bivariate Data Displays are about the types of variable in given displays.  By reviewing student answers, I can quickly evaluate whether they understand the relationship between variable type and display type for bivariate data sets.
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