AP Statistics Two Categorical Variables and Two-Way Tables Test Solutions and Scoring (PDF)

AP Statistics math test solutions: Two Categorical Variables and Two-Way Tables – Maths PDF

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This two categorical test answers 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.

Each solution is followed by a scoring guide. Give credit for choosing the correct denominator, for the correct percent, and for an interpretation that compares groups in context.

AP Statistics · Common Core State Standards: AP STAT 2.1, AP STAT 2.2, AP STAT 2.3, HSS-ID.B.5

Two categorical test answers: worked solutions

Question 1 – Marginal and joint [3 pts]

Sports participation.

(a) \(\frac{70}{150}\approx 46.7\%\). (b) \(\frac{25}{150}\approx 16.7\%\). (c) 60.

46.7%; 16.7%; 60.

Scoring: 1 point per part.

Question 2 – Conditional percents [3 pts]

Grade 9: \(\frac{45}{60}=75\%\). Grade 12: \(\frac{25}{90}\approx 27.8\%\).

75% compared with 27.8%. Yes, there is an association: Grade 9 students are much more likely to play a sport.

Scoring: 1 point for each percent; 1 point for the conclusion with numbers.

Question 3 – Segmented bar graph [3 pts]

Membership renewals.

(a) A: \(0.70\times 300=210\). B: \(0.50\times 200=100\).

(b) No, an association does not show causation.

210 and 100; no.

Scoring: 1 point for each count; 1 point for the explanation.

Question 4 – Choose the denominator [2 pts]

Seniors: \(\frac{18}{90}=20\%\). Juniors: \(\frac{12}{60}=20\%\).

The percents are equal (20%), so seniors are not more likely to join; there are just more seniors.

Scoring: 1 point for both percents; 1 point for the conclusion.

Question 5 – Simpson's paradox [3 pts]

Overall: A \(\frac{84}{100}=84\%\), B \(\frac{47}{100}=47\%\). Mild: A 90%, B 95%. Severe: A 30%, B 35%.

Hospital A is better overall (84% compared with 47%) but B is better in both severity levels (95% compared with 90%, 35% compared with 30%). Severity is a lurking variable.

Scoring: 1 point for overall rates, 1 point for rates within each group, 1 point for the explanation.

Question 6 – Complete a table [2 pts]

Grade 11 total: \(80-50=30\). Not in band: \(30-12=18\).

18 students.

Scoring: 1 point for the Grade 11 total, 1 point for 18.

Question 7 – Explain a vocabulary term [2 pts]

A conditional relative frequency is a cell count divided by the total of the group you are given.

Example: among Grade 9 students, 45/60 = 75% play a sport.

Scoring: 1 point for the definition; 1 point for a correct example.

Question 8 – Missing counts [2 pts]

Under 30 in summer: \(55-30=25\).

25 people.

Scoring: 1 point for the setup using the total 55; 1 point for 25.

Total score

Total

20 points

Key facts behind this two categorical test answers

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 answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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