Analyzing Categorical Data
Chapter 1 - Day 3 - Lesson 1.1
Identify the individuals and variables in a set of data.
Classify variables as categorical or quantitative.
Make and interpret bar graphs for categorical data.
Identify what makes some graphs of categorical data misleading.
Calculate marginal and joint relative frequencies from a two-way table.
Calculate conditional relative frequencies from a two-way table.
Use bar graphs to compare distributions of categorical data.
Describe the nature of the association between two categorical variables.
New Activity: How are your favorite classes related?
Archived Activity: What was your favorite toy?
We have a VERY ambitious list of learning targets today. But by the end of the activity and notes, we will have hit all of them. This is really why we love doing activities with students. We’ve had many long debates about what as teachers do we owe students. To hit 8 learning targets, do we need pages and pages of notes so that students are completely, 100% prepared for any and all possible variations of the questions that could show up on the test? We would argue, “no.” While we want to, of course, prepare students for assessments, we know there is so much more to learning than memorizing and taking notes. With this activity, you will see how students can learn through experiencing statistics. This will help them to develop a deeper conceptual understanding and flexible thinking. After completing the activity in groups, the teacher will go through and formalize the learning in the activity by adding information to the margins. Instead of traditional notes, we use an “Important Ideas” section as a space for the teacher to add in any necessary vocabulary or formulas. Finally, we end with a “Check your Understanding” section for students to complete in their groups. This gives them a chance to practice what they learned.
How do we possibly do all of that in one day? The key is to be as efficient and succinct as possible. It’s important to note that we may not cover every learning target in the activity. But if we don’t hit something in the activity, we make sure it is in the “Important Ideas”. Think about your lessons as more than just your notes. Our goal is to fully meet all learning targets with the activity, notes, and even homework, but not necessarily each target on each part. We make sure to tell you this so that you don’t only use the activity or only use the notes. We’ve designed our lessons to be used in their entirety.
So for today’s lesson we are going to begin by collecting some data. Make sure students are in groups (we like groups of 4). Ask the students to pick which of the electives is their favorite. They must pick one. Give them 1 minute to talk about this in their groups. By letting them get all their talking out right away, it will be easier to stay on task later. Then have students come to the board to mark their favorite elective. Later in the activity students will need to also pick whether they prefer math or English. You could collect this data now, or have them raise their hands later.
After collecting data, students should be able to work through the entire activity without teacher input. Circulate throughout the room and help students as needed. Have groups put their work on the board and discuss answers with the class. Add in formal language in the margins. You will see on our key that there is information written in another color in the margins. This is what we added during the Activity debrief. This is how we formalize the activity experience. Make sure to be transparent about this to students. Explain what you’re doing and have them write it in as well.
After completing the activity, use direct instruction to fill in some of the margin notes and the “Big Ideas” text box. Give students the rest of the time to work on the “Check your understanding” We know from the past years that students will struggle with marginal and conditional probability. We’ve included more practice on the note page and in the homework. Spend extra time on this. Also, the activity did not cover misleading graphs so we will look at those on the notes.
Students will need devices with internet access to complete the Activity. Before starting the Activity, you may want to introduce students to the applet they will be using. We’d suggest showing them a few of the basic functions that will be needed for chapter 1, like how to enter data and make a graph. You may consider working through the first graph (Activity question #4) together, but then let students figure out the other graphs in their groups.