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# Creating Two-Way Tables

Lesson 11 of 19

## Objective: SWBAT construct a two-way frequency table and determine marginal, joint and conditional frequencies.

## Big Idea: Students collect qualitative data in real-time, construct and analyze a two-way table, then make a generalization to a larger population.

*45 minutes*

#### Opening

*10 min*

When students enter the room today, they are asked to write down their favorite extra-curricular activity. I plan to call on a few students to get a sense of some of the ideas in the room. Then I ask students to identify the three main phases of statistics:

- Collect Data
- Organize Data
- Analyze Data

After we discuss their ideas, I ask students to try to write down these three phases above in their notebooks.

I then ask students to make a plan for organizing the data about extra-curricular activities that was collected at the start of class. I ask students to work in their pairs to decide how we can organize the data. Usually a few groups will quickly realize that to list every activity would be too cumbersome. Many will start grouping activities by topic would be best.

As students work on organizing the data, I make note of the ideas that they pursue. I keep track of them and I make a plan to call on specific groups to share out with the class later in the lesson.

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#### Direction Instruction

*5 min*

After students have explored the raw data and come up with plans for organizing it, I will make (or display) a table like the one shown in slide 3 of Two-Way_Table. Next, I plan to use this table to tally the data from the students in the classroom: What is your favorite extra-curricular activity? After surveying each student, we will tabulate the data and record the totals in each cell.

Looking at the completed table, I will explain to the class that we have just found the joint frequencies for this table. The joint frequencies represent values that have two attributes in common (e.g., Male and Athletics). The students will move on to phase 3 (analyze the data) in a moment. Before moving on, I will answer any questions that the students have about the organization of the data and the meaning of conditional frequency.

#### Resources

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#### Investigation

*25 min*

For this investigation, students will work in pairs. I will begin by distributing Two_Way_Table to the class. As I handout this resource, I remind my students that they are responsible for the vocabulary on the worksheet. (The terms that are considered **new vocabulary** are bold and underlined). I also encourage students to read all directions carefully. I suggest that it is a good idea to discuss the meaning of vocabulary words with their partners.

Organizating data is challenging for some students. For those students, I let them use a computer or ipad in the room to watch the following video and learn more.

**Source URL**: https://www.youtube.com/watch?v=CKWDRYHgbgA (Accessed May 10 2014)

To extend this lesson, I ask some students to visualize the question from another perspective. I may ask them to make an inference:

**If we had asked 200 students from our school the same question, how many students do you think would be in each cell of the table?**

This type of question gets students thinking ahead to the focus of our next lesson. What does it mean to sample a population and then extend the results to a larger population?

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#### Closure

*5 min*

For a closing prompt today, I ask students:

- What are the three types of relative frequencies?
- What questions do you still have about this lesson?

These prompts will help me to appreciate which students grasp the vocabulary at a basic level?Which students have a more sophisticated grasp on the vocabulary?

Based on the results from the Ticket out the Door, some time may need to be spent at the beginning of the next lesson to re-visit the vocabulary terms.

#### Resources

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- LESSON 1: Asking a Statistical Question
- LESSON 2: Measures of Center
- LESSON 3: Practice with Measures of Central Tendency
- LESSON 4: Organizing Data with a Box Plot
- LESSON 5: Understanding Box Plots (with Assessment)
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- LESSON 12: More with Conditional, Joint, and Marginal Frequencies
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- LESSON 14: A Bivariate Relationship
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