AP Statistics Two Categorical Variables and Two-Way Tables Test with Point Values (PDF)
This two categorical test for AP Statistics covers two categorical variables and two-way tables (Common Core AP STAT 2.1, AP STAT 2.2, AP STAT 2.3, HSS-ID.B.5), with a free PDF to print.
Time and points
- Grade: AP Statistics
- Chapter: Two Categorical Variables and Two-Way Tables
- Standards: AP STAT 2.1, AP STAT 2.2, AP STAT 2.3, HSS-ID.B.5
- Time: 45 minutes
- Total: 20 points
Two categorical test: questions
Question 1 – Marginal and joint [3 pts]
(a) Find the marginal relative frequency of students who play a sport. (1 point) (b) Find the percent of all students who are in Grade 12 and play a sport. (1 point) (c) Complete: the number of Grade 9 students is ___. (1 point)
Question 2 – Conditional percents [3 pts]
Use the sports table. Find the percent of Grade 9 students who play a sport and the percent of Grade 12 students who play a sport. (2 points) Is there an association? (1 point)
Question 3 – Segmented bar graph [3 pts]
Gym A has 300 members and Gym B has 200 members. (a) How many renewed at each gym? (2 points) (b) Does the graph show that Gym A causes renewals? Explain. (1 point)
Question 4 – Choose the denominator [2 pts]
In a table, 18 of 90 seniors and 12 of 60 juniors are in a club. A student claims the club has more seniors, so seniors are more likely to join. Respond using percents.
Question 5 – Simpson's paradox [3 pts]
Hospital A treats 90 mild cases (81 recover) and 10 severe cases (3 recover). Hospital B treats 20 mild cases (19 recover) and 80 severe cases (28 recover). Compare the overall recovery rates, then the rates within each severity level.
Question 6 – Complete a table [2 pts]
A table of 80 students has 50 in Grade 10, of whom 30 take band. In Grade 11, 12 take band. Find the number in Grade 11 who do not take band.
Question 7 – Explain a vocabulary term [2 pts]
Define conditional relative frequency and give an example from the sports table.
Question 8 – Missing counts [2 pts]
A survey of 120 people shows 70 prefer summer. Of the 50 who prefer winter, 30 are under 30 years old. If 55 people are under 30 in all, how many people who prefer summer are under 30?
Key facts behind this two categorical test
- Two-way tables show counts for combinations of two categorical variables.
- Marginal = total / grand total; joint = cell / grand total; conditional = cell / group total.
- Compare conditional percentages of the response across explanatory groups to detect association.
- Segmented bar graphs display conditional distributions side by side.
- Association is not causation, and combined data can hide Simpson’s paradox.
How to use this two categorical test
Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.
All AP Statistics chapters: AP Statistics math.
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AP Statistics Two Categorical Variables and Two-Way Tables Test with Point Values
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