Lesson 9: Looking for Associations

Let’s look for associations in data.

9.1: Notice and Wonder: Bar Association

What do you notice? What do you wonder?


 

9.2: Matching Representations Card Sort

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 25 35 60
13 to 15 years old 40 10 50
16 to 18 years old 50 10 60
total 115 55 170
 

Some cards show bar graphs like this:

Some cards show segmented bar graphs like this:

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.

9.3: Building Another Type of Two-Way Table

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 25 35 60
13 to 15 years old 40 10 50
16 to 18 years old 50 10 60
total 115 55 170

  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.

      has cell phone does not have cell phone total
    10 to 12 years old 42%    
    13 to 15 years old     100%
    16 to 18 years old   17%  

    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?

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.

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.

  meditated did not meditate total
calm 45 8 53
agitated 23 21 44
total 68 29 97

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.


 
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 66% 28%
agitated 34% 72%
total 100% 100%


 

Practice Problems ▶

Glossary

segmented bar graph

segmented bar graph

A segmented bar graph compares two categorical variables by showing one of the categories on the horizontal axis and representing the percentages in the other category with stacked vertical bars.

relative frequency

relative frequency

See frequency.

two-way table

two-way table

A two-way table provides a way to investigate the connection between two categorical variables.

It shows one of the variables across the top and the other down the side. Each entry in the table is the frequency or relative frequency for the corresponding pair of categories.

The two-way table shows the results of a study of the connection between meditation and state of mind of athletes before a track meet.

  meditated did not meditate total
calm 45 8 53
agitated 23 21 44
total 68 29 97