AP Statistics Unit 2 Exploring Two-Variable Data

Topic 2.3: Statistics for Two Categorical Variables

Joint, Marginal, and Conditional Relative Frequencies
Video Follow-Along Worksheet
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Learning Objectives: Essential Knowledge:

Key Vocabulary

Joint Relative FrequencyA cell count divided by the total number of observations in the table.
Marginal Relative FrequencyA row total or column total divided by the table total.
Conditional Relative FrequencyA relative frequency found within a specific row or column of a two-way table.
Row TotalThe total for one row of a two-way table.
Column TotalThe total for one column of a two-way table.
Table TotalThe grand total of all observations in the two-way table.
DistributionHow the values of a categorical variable are divided among its categories.
AssociationA relationship in which knowing one categorical variable helps predict another.
Two-Way TableA table that summarizes two categorical variables at the same time.
Segmented Bar GraphA graph that shows conditional relative frequencies stacked to 100% for each group.

Video 1: Statistics for Two Categorical Variables

[0:00 – 8:53]
1. [0:09] The video focuses on how to calculate summary for two categorical variables and how to use them to determine whether there is an .
Age Group and Educational Attainment Example [0:31 – 1:10] The same two-way table from the last two lessons returns here. Age group is arranged across the top of the table, and educational attainment is listed down the side.
2. [0:31] The two categorical variables in the example are and .
3. [0:42] In the previous lesson, graphical displays showed that the two variables were .
4. [1:10] Before calculating percents, the speaker finds the , the , and the .
Statistic Numerator Denominator
Joint relative frequency One cell count Table total
Marginal relative frequency Row total or column total Table total
Conditional relative frequency One cell count in a chosen group That row or column total
5. [1:39] To find the percent of people who are 25 to 34 years old with a master's degree or higher, divide the cell count by the .
6. [2:27] A cell frequency divided by the total for the entire table is called a .
7. [2:08] In the example, that joint relative frequency is about .
8. [2:50] To find the percent of people in the survey who have only a high school diploma, use the and divide by the table total.
9. [4:05] A row total or column total divided by the table total is a .
10. [2:50] The marginal relative frequency for people with only a high school diploma is about .
11. [3:32] The percent of people in the survey who are 35 to 54 years old uses the divided by the table total.
12. [3:32] That marginal relative frequency is about .
Joint vs. Marginal Relative Frequency [1:39 – 4:05]
13. [4:33] The phrase "of those with only a high school diploma" means the calculation stays within one .
14. [4:33] The percent of people with only a high school diploma who are 35 to 54 years old is about .
15. [5:13] The phrase "of those 25 to 34 years old" means the calculation stays within one .
16. [5:13] The percent of 25- to 34-year-olds who have no high school diploma is about .
17. [5:49] Relative frequencies calculated within a specific row or column are called .
Conditional Relative Frequency Rule [4:33 – 6:20]
18. [6:20] In the previous lesson, the class used conditional relative frequencies to find the of educational attainment within each age group.
19. [7:04] In the segmented bar graph, the conditional relative frequencies for each are stacked on top of one another.
20. [7:27] The segmented bar graphs for the age groups were not the .
21. [7:53] Because the distributions of conditional relative frequencies are for the age groups, the variables are .
22. [8:28] To decide whether two categorical variables are associated, the most important summary statistics are the .
23. Reflection: How is a marginal relative frequency different from a conditional relative frequency?
24. Reflection: Why are conditional relative frequencies the best summary statistics for deciding whether two categorical variables are associated?

Exit Ticket

A school surveyed students about grade level and preferred study style. The results are shown below.

Study Preference 9th Grade 10th Grade 11th Grade Total
Prefers studying alone 18 12 10 40
Prefers studying with a group 12 18 30 60
Total 30 30 40 100

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

(b) Find the joint relative frequency for a student who is in 11th grade and prefers studying with a group.

(c) Find the marginal relative frequency for 10th grade.

(d) Find the conditional distribution of study preference within 9th grade and within 11th grade.

(e) Use those conditional relative frequencies to decide whether grade level and study preference are associated.

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