# Categorically Quantified

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## Objective

SWBAT represent and interpret data for quantitative or qualitative (categorical or measurement) variables

#### Big Idea

What kind of data do I have and what can I do with it? Figure out how to work with both qualitative and quantitative data sets.

## Set the Stage

15 minutes

You will need copies of the student survey data handout ready for this lesson.  I begin class with a blank student survey data chart projected or drawn on my front board.  As the bell rings, I give my students directions to each fill in one line of the chart based on their personal data and preferences.  There are always a few who need clarification about such things as whether or not sandals count as shoes or if they can add a color to the list.  I answer their questions (no, they can’t add a color) then tell my students they will be working independently for this first section of the lesson.  I pass out the handout and ask them to copy the data from the board.

When everyone is done, I ask them to look over the types of data we've collected and decide whether each is categorical or quantitative.  These are terms they should already be familiar with from earlier classes, so this is a good opportunity to refresh their memories and check for understanding.  I randomly call on students (you can see my methods for randomly selecting students in my strategies folder) to share their thoughts on how to classify each data set and why they chose as they did.  I allow for class discussion and ask leading questions as necessary, to get my students to recognize that gender and favorite color are the two categorical data sets.

I then ask them to think-pair-share (you can see my methods for pair-share partners in my strategies folder) what methods they could use to make the data easier to understand.  As they talk, I walk around to get a sense of what they're thinking.  This helps me be ready for our class discussion by letting me know if my students are mostly focused on graphs and charts or if they're thinking about finding numeric summaries. After a few minutes I ask that one member of each team write the ideas they discussed on the front board.  I keep enough markers for several students to be writing at the same time to facilitate activities like this.  When all the teams have posted their ideas, I help the class summarize what they've posted and ask leading questions like "Is there any way to make this list of numbers easier to understand?" and "What others ways have you summarized lists of numbers before?" to edit as necessary.  My goal for this activity is that my students suggest finding an average, finding a range, and maybe even making a boxplot, stem-and-leaf plot or dotplot.

## Put it into Action

35 minutes

Teamwork 20min: see video

Class Discussion 10min: When all the teams have completed their summary work I select teams based on what I've observed as they were working to briefly present their summaries to the class.  I look for teams that have used incorrect analyses for the categorical data sets so that we can discuss what works.  If all of my teams choose correctly, then I have them present and we discuss why/how they made the choices they did.  There is almost always at least one team that finds the "average" for the colors because I assigned them numbers.  This allows for a good discussion about categorical vs quantitative data. (MP2) Another interesting area of discussion comes when a team summarizes the number of pairs of shoes with a decimal number or fraction.  This generates dialogue about what the summary numbers represent and lets my students explore other types of data that should be represented with positive integers.

## Wrap it Up

10 minutes

To really cement the idea that not all data sets are created equal, I give each student a notecard and ask them to list at least three categorical and three quantitative data sets and explain why each fits where it does.