AP Statistics Unit 2 Exploring Two-Variable Data

Topic 2.2: Representing Two Categorical Variables

Two-Way Tables, Side-by-Side Bar Graphs, Segmented Bar Graphs, and Mosaic Plots
Video Follow-Along Worksheet
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Learning Objectives: Essential Knowledge:

Key Vocabulary

Two-Way TableA table that summarizes the relationship between two categorical variables.
Contingency TableAnother name for a two-way table.
Relative FrequencyA proportion or percent found by dividing a count by an appropriate total.
Conditional Relative FrequencyA relative frequency found within a single row or column category.
Joint Relative FrequencyA cell count divided by the total number of observations in the entire table.
DistributionHow the values of a categorical variable are divided among its categories.
Side-by-Side Bar GraphA display with separate bars for each category within each group.
Segmented Bar GraphA display made by stacking the bars for a group so the total height is 100%.
Mosaic PlotA segmented bar graph whose bar widths represent group sizes.
AssociationA relationship in which knowing one categorical variable helps predict another.

Video 1: Representing Two Categorical Variables

[0:00 – 7:21]
1. [0:10] The lesson asks how to create graphical displays for two variables and how to decide whether those variables are .
Age Group and Educational Attainment Example [0:33 – 0:49] The video revisits a two-way table about age group and educational attainment. The age-group columns are 25 to 34, 35 to 54, and 55 years or older, and each column is broken into four educational attainment levels.
2. [0:33] A table that summarizes two categorical variables is called a and also a .
3. [0:33] In this example, the two variables are and .
4. [1:19] Before making displays, the speaker first finds the for each .
Age Group Column Total Used for Percents
25 to 34 45,212
35 to 54 93,506
55 years or older Use that column's total
5. [1:42] To find the educational attainment distribution within the 25 to 34 group, divide each count by the .
6. [2:21] For the 35 to 54 group, each percentage is still found by dividing by the .
How the Percents Are Built [1:19 – 2:49]
7. [2:49] After the percents are calculated, they are used to create a bar graph.
8. [2:51] Each age group is represented by bars because there are four educational attainment levels.
9. [3:31] A segmented bar graph is created by the bars for each group on top of one another.
10. [3:49] In a segmented bar graph, each bar goes all the way up to .
11. [4:33] A mosaic plot is a segmented bar graph in which the bar depends on the size of the group.
12. [4:33] The segmented bar graph does not show the of the groups, but the mosaic plot does.
Display How It Is Built What It Adds
Side-by-side bar graph Separate bars for each group Lets you compare percents category by category
Segmented bar graph Stacks each group's bars to 100% Makes the overall distributions easy to compare
Mosaic plot Uses a segmented bar graph with varying widths Shows both distributions and group sizes
13. [5:12] The 25 to 34 age group has the width because it is the smallest group.
14. [5:41] To decide whether the variables are related, compare the across the age groups.
15. [5:41] If knowing a person's age group helps predict educational attainment, then the variables are .
Rule for Association [5:41 – 7:02]
16. [6:36] The three displays emphasized in the lesson are side-by-side bar graphs, segmented bar graphs, and plots.
17. [7:02] If the distributions are for each group, then there is an association.
18. [7:02] Graphical displays of two categorical variables are used to compare and determine whether the variables are associated.
19. Reflection: Why does dividing by the column total help when comparing educational attainment across age groups?
20. Reflection: How can a segmented bar graph or mosaic plot help you decide whether two categorical variables are associated?

Exit Ticket

A school surveyed students about grade level and whether they play a school sport. The results are shown below.

Sport Participation 9th Grade 10th Grade 11th Grade
Plays a school sport 18 24 14
Does not play a school sport 12 16 36
Total 30 40 50

(a) Identify the two categorical variables and explain why this is a two-way table.

(b) Find the conditional distribution of sport participation within 9th grade and within 11th grade.

(c) If you made a segmented bar graph from these percents, would the bars look the same or different? What would that tell you about association?

(d) Explain one reason a mosaic plot could be more informative than a segmented bar graph for this data.

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