Using Data Displays

to Find Associations

Lesson 10

Let’s use data displays to find associations!

Today’s Goal

• I can create relative frequency tables, bar graphs, and segmented bar graphs from frequency tables to find associations among variables.

Sports and

Musical Instruments

Warm Up

For a survey, students in a class answered these questions:

• Do you play a sport?
• Do you play a musical instrument?

Please begin working on your own. (2 min)

What percentage of students who play a sport don’t play a musical instrument?

What percentage of students who don’t play a sport also don’t play a musical instrument?

Sports and Music Association

Activity 1

• MLR1: Stronger and Clearer Each Time
• Think Pair Share

Here’s the data from today’s Warm Up.

One partner should work on Problems 1-2, while the other works on Problems 3-4. (5-10 min) Then work together to complete the last problem.

What different information can be seen by the two segmented bar graphs?

Why are the numbers in the top left box in the two tables different?

What do they mean?

Is there an association between the two variables? Explain.

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What would the segmented bar graphs look like if there was no association?

What would the segmented bar graphs look like if there way an association?

Colored Erasers

Activity 2

• MLR6: Three Reads
• Think Pair Share

1st Read: Shared Reading�What is this situation about?

2nd Read: Team Reading�What do the values and labels in the table mean?

3rd Read: Team Reading�Read the questions in the task. �How might you get started?

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Start working on your own. (5 min) �Then we’ll discuss your thinking in teams!

What strategies did you use to create the segmented bar graphs?

Are the flawed erasers associated with certain colors?

Explain your reasoning.

Do you think that noticing the association was easier with one of the graphs?

If there was not an association between color and flaws, what might the segmented bar graph based on the rows look like?

If there was not an association between color and flaws, what might the segmented bar graph based on the columns look like?

Are you ready for more?

Based on the federal budget for 2009, the table shows where some of the federal money was expected to go. The values are in billions of U.S. dollars.

1. Why would a segmented bar graph be more useful that the table of data to see any associations between the country and where the money is spent?
2. Create a segmented bar graph that represents the data from the table.
3. Is there an association between the country’s budget and their spending? Explain.

We have been looking for associations in categorical data.

There is evidence of an association if the relative frequencies of some characteristics are very different from each other in different groups!

Is it easier to see evidence of an association in a frequency table or a relative frequency table?

It depends on the data…

If the two groups are approximately the same size, it doesn’t matter much.

But when they are different sizes, it is usually easier to compare using relative frequencies.

How can we see evidence of an association in a two-way table of either kind?

By numerically comparing the proportions between the two groups.

How can we see evidence of an association in a bar graph or segmented bar graph?

By visually comparing the proportions between the two groups.

Today’s Goal

• I can create relative frequency tables, bar graphs, and segmented bar graphs from frequency tables to find associations among variables.

Class Preferences

Cool Down