AP Statistics Two Categorical Variables and Two-Way Tables Worksheet (PDF)
This two categorical worksheet 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.
AP Statistics · Common Core State Standards: AP STAT 2.1, AP STAT 2.2, AP STAT 2.3, HSS-ID.B.5
Two categorical worksheet: exercises 1 to 10
Exercise 1 – Explanatory and response
Name the explanatory and response variable. (a) Researchers ask whether the type of breakfast (cereal, eggs, none) is related to alertness (alert or not) in class. (b) A school asks whether the grade level affects whether students buy lunch.
Exercise 2 – Complete the table
A survey of 100 students asked whether they own a bike. Of the 40 sophomores, 24 own a bike. Of the 60 juniors, 30 own a bike. Complete a two-way table.
Exercise 3 – Marginal relative frequency
Find the marginal relative frequency of students who read daily, and of students in Grade 10.
Exercise 4 – Joint relative frequency
Using the table of 200 students, find the percent of all students who are in Grade 11 and do not read daily.
Exercise 5 – Conditional given a column
Of the Grade 9 students, what percent read daily? Of the Grade 11 students?
Exercise 6 – Conditional given a row
Of the students who read daily, what percent are in each grade?
Exercise 7 – Segmented bar graph
Make a segmented bar graph of the reading habit within each grade and describe any association.
Exercise 8 – Read a segmented bar graph
The graph compares the percent of students passing a class under two phone policies (200 students each). How many in each group passed? Is there an association?
Exercise 9 – Which direction?
In a study of 500 adults, 60 of the 150 smokers and 40 of the 350 nonsmokers have a cough. Find the percent of smokers who cough and the percent of coughers who smoke.
Exercise 10 – Build a table from percents
A school has 400 students. Fifty percent are girls. Of the girls, 30% are in band; of the boys, 20% are in band. Make the two-way table of counts.
Exercises 11 and up
Exercise 11 – Simpson's paradox: the data
Two tutoring programs are compared by pass rates. In the easy course, Program X: 72 of 80 passed; Program Y: 10 of 10 passed. In the hard course, Program X: 2 of 20 passed; Program Y: 12 of 90 passed. Find the pass rate for each program in each course and overall.
Exercise 12 – Explain the paradox
Explain why Program X looks better overall in the previous problem even though Program Y has the higher pass rate in each course.
Exercise 13 – Association or not?
In a sample, 30% of boys and 30% of girls prefer online classes. Are sex and class preference associated? Explain.
Exercise 14 – Causation
A study finds that students who eat breakfast have a higher percent of passing grades. A news story says breakfast improves grades. Is that justified? Explain.
Exercise 15 – Pet ad
Some owners rated a pet-store ad. Find the percent of cat owners who like the ad and the percent of dog owners who like it. Is there an association?
Exercise 16 – Describe the association
Write two sentences describing the association in the pet-ad table using conditional percents.
Exercise 17 – Fill in with totals
A survey of 250 people shows 140 are female. Of 90 people who prefer tea, 63 are female. Find the number of males who prefer coffee (assuming only tea or coffee).
Exercise 18 – Expected counts preview
If sex and drink preference were unrelated, the percent of females preferring tea would equal the overall percent preferring tea (90 of 250). Find the expected number of females who prefer tea among the 140 females, and compare with 63.
Exercise 19 – Multi-step
A county reports that 1,200 of 4,000 teenagers vape. Among the 1,500 teens from rural areas, 540 vape. Find the percent of rural teens who vape and of non-rural teens who vape.
Exercise 20 – Percent of a group
At a school, 35% of the 600 students ride the bus. Of the bus riders, 40% are in grade 9. How many bus riders are in grade 9, and what percent of all students is that?
Key facts behind this two categorical worksheet
- 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 worksheet
Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.
Download the two categorical worksheet as a PDF with the button below and keep it with your notes.
Download the two categorical worksheet as a PDF with the button below and keep it with your notes.
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