Lesson 23Looking for Associations

Learning Goal

Let’s look for associations in data.

Learning Targets

  • I can identify the same data represented in a bar graph, a segmented bar graph, and a two-way table.

  • I can use a two-way frequency table or relative frequency table to find associations among variables.

Lesson Terms

  • relative frequency
  • segmented bar graph
  • two-way table

Warm Up: Notice and Wonder: Bar Association

Problem 1

What do you notice? What do you wonder?

A bar graph of "plays sports" vs "no sports" and "watches tv" and "not much tv".

Activity 1: Matching Representations Card Sort

Problem 1

Your teacher will hand out some cards.

Some cards show two-way tables like this:

has cell phone

does not have cell phone

total

10 to 12 years old

13 to 15 years old

16 to 18 years old

total

Some cards show bar graphs like this:

A bar graph of 10-12, 13-15, and 16-18 year olds and "has cell phone" vs "no cell phone"

Some cards show segmented bar graphs like this:

A segmented bar graph of 10-12, 13-15, and 16-18 year olds and "has cell phone" vs "no cell phone"

The bar graphs and segmented bar graphs have their labels removed.

  1. Put all the cards that describe the same situation in the same group.

  2. One of the groups does not have a two-way table. Make a two-way table for the situation described by the graphs in the group.

  3. Label the bar graphs and segmented bar graphs so that the categories represented by each bar are indicated.

  4. Describe in your own words the kind of information shown by a segmented bar graph.

Are you ready for more?

Problem 1

One of the segmented bar graphs is missing. Construct a segmented bar graph that matches the other representations.

Activity 2: Building Another Type of Two-Way Table

Problem 1

Here is a two-way table that shows data about cell phone usage among children aged 10 to 18.

has cell phone

does not have cell phone

total

10 to 12 years old

13 to 15 years old

16 to 18 years old

total

  1. Complete the table. In each row, the entries for “has cell phone” and “does not have cell phone” should have the total 100%. Round entries to the nearest percentage point.

    This is still a two-way table. Instead of showing frequency, this table shows relative frequency.

    has cell phone

    does not have cell phone

    total

    10 to 12 years old

    13 to 15 years old

    16 to 18 years old

    This is still a two-way table. Instead of showing frequency, this table shows relative frequency.

  2. Two-way tables that show relative frequencies often don’t include a “total” row at the bottom. Why?

  3. Is there an association between age and cell phone use? How does the two-way table of relative frequencies help to illustrate this?

Are you ready for more?

Problem 1

A pollster attends a rally and surveys many of the participants about whether they associate with political Party A or political Party B and whether they are for or against Proposition 3.14 going up for vote soon. The results are sorted into the table shown.

for

against

party A

party B

  • A news station reports these results by saying, “A poll shows that about the same number of people from both parties are voting against Proposition 3.14.”

  • A second news station shows this graphic.

A segmented bar graph for party A and party B showing for and against the proposition.
  1. Are any of the news reports misleading? Explain your reasoning.

  2. Create a headline, graphic, and short description that more accurately represents the data in the table.

Lesson Summary

When we collect data by counting things in various categories, like red, blue, or yellow, we call the data categorical data, and we say that color is a categorical variable.

meditated

did not meditate

total

calm

agitated

total

We can use two-way tables to investigate possible connections between two categorical variables. For example, this two-way table of frequencies shows the results of a study of meditation and state of mind of athletes before a track meet.

If we are interested in the question of whether there is an association between meditating and being calm, we might present the frequencies in a bar graph, grouping data about meditators and grouping data about non-meditators, so we can compare the numbers of calm and agitated athletes in each group.

A bar graph of meditated vs did not meditate and calm vs agitated.

Notice that the number of athletes who did not meditate is small compared to the number who meditated (29 as compared to 68, as shown in the table).

If we want to know the proportions of calm meditators and calm non-meditators, we can make a two-way table of relative frequencies and present the relative frequencies in a segmented bar graph.

meditated

did not meditate

calm

agitated

total

A segmented bar graph showing meditated vs did not meditate and calm vs agitated.