AP Statistics Two Categorical Variables and Two-Way Tables Test with Point Values (PDF)

AP Statistics math test: Two Categorical Variables and Two-Way Tables – Maths PDFCover of the book AP Statistics Math Tests with Answer Keys (PDF)Download as a PDFThe AP Statistics tests book with answer keysPrintable PDFSee the book ›


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.

This 45-minute test covers two-way tables, the three kinds of relative frequency, segmented bar graphs, and association. Show each division and state your conclusions in context.

Time and points

About this test
  • 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]

Sport \ GradeGrade 9Grade 12TotalPlays a sport452570No sport156580Total6090150
Sports participation.

(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]

Sport \ GradeGrade 9Grade 12TotalPlays a sport452570No sport156580Total6090150
Sports participation.

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]

0%20%40%60%80%100%Percent70%30%Gym A50%50%Gym BRenewedLeftGym
Membership renewals.

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?

See the solutions: Two Categorical Variables and Two-Way Tables test solutions

Key facts behind this two categorical test

Key facts
  • 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.

Voter.. post

Free printable PDF

AP Statistics Two Categorical Variables and Two-Way Tables Test with Point Values

US Letter75 KBPrints in black and white

Download PDF