AP Statistics Variables and Categorical Data Displays Test Solutions and Scoring (PDF)

AP Statistics math test solutions: Variables and Categorical Data Displays – Maths PDF

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This categorical data test answers for AP Statistics covers variables and categorical data displays (Common Core AP STAT 1.1, AP STAT 1.2, AP STAT 1.3, HSS-ID.A.1), with a free PDF to print.

Each solution includes a scoring guide with partial credit. Award the points for the correct calculation and for the sentence that interprets the answer in context.

AP Statistics · Common Core State Standards: AP STAT 1.1, AP STAT 1.2, AP STAT 1.3, HSS-ID.A.1

Categorical data test answers: worked solutions

Question 1 – Variable types [2 pts]

Quantitative
Categorical
Categorical
Quantitative

Quantitative, categorical, categorical, quantitative.

Scoring: 0.5 point for each correct classification.

Question 2 – Frequency table [3 pts]

Percent of households.

(a) \(30+22+8+10=70\) households.

(b) \(\frac{30}{70}\approx 42.9\%\), \(\frac{22}{70}\approx 31.4\%\), \(\frac{8}{70}\approx 11.4\%\), \(\frac{10}{70}\approx 14.3\%\).

70 households; 42.9%, 31.4%, 11.4%, 14.3%.

Scoring: 1 point for the total; 1 point for the correct method (count divided by total); 1 point for all four correct percents (allow one rounding slip).

Question 3 – Missing category [2 pts]

Water: \(100\%-48\%-30\%-14\%=8\%\).

\(0.08\times 200=16\).

16 adults.

Scoring: 1 point for 8%; 1 point for 16.

Question 4 – Pie chart [2 pts]

Slices in degrees.

Food: \(0.25\times 360^{\circ}=90^{\circ}\). Fun: \(0.15\times 360^{\circ}=54^{\circ}\).

90 and 54 degrees.

Scoring: 1 point for each correct angle.

Question 5 – Compare groups [3 pts]

(a) Boys: \(0.60\times 50=30\). Girls: \(0.75\times 80=60\).

(b) The groups have different sizes, so counts would not compare fairly.

30 boys and 60 girls; use percents because the group sizes differ.

Scoring: 1 point for each count; 1 point for a correct explanation about group size.

Question 6 – Appropriate display [2 pts]

Students can pick several clubs, so the percents can add to more than 100%. A pie chart requires the parts to make one whole.

Use a bar graph.

Scoring: 1 point for the reason (percents do not add to 100%); 1 point for naming a bar graph.

Question 7 – Misleading graph [2 pts]

Visible heights: \(78-75=3\) and \(84-75=9\), so the bar looks \(\frac{9}{3}=3\) times as tall.

Actual: \(\frac{84}{78}\approx 1.08\).

3 times as tall; actually about 1.08 times as large.

Scoring: 1 point for the apparent ratio 3; 1 point for the actual ratio about 1.08.

Question 8 – Find the total [2 pts]

\(n=\frac{63}{0.21}=300\).

300 students.

Scoring: 1 point for setting up 0.21n = 63; 1 point for 300.

Question 9 – Describe the distribution [2 pts]

Percents: \(\frac{100}{250}=40\%\), \(\frac{90}{250}=36\%\), \(\frac{60}{250}=24\%\).

Online classes were most popular (40% of the 250 students), followed closely by in-person (36%); hybrid was least popular at 24%.

Scoring: 1 point for the correct percents; 1 point for a sentence that uses context and names most and least popular.

Total score

Total

20 points

Key facts behind this categorical data test answers

Key facts

Individuals are the objects described by data; a variable is a trait that varies among them.
Categorical variables name groups; quantitative variables are measured with numbers.
Relative frequency = category count divided by total, and relative frequencies add to 1.
Bar graphs have a zero baseline and gaps between bars; pie charts need parts of one whole.
Compare different-sized groups with percents, not raw counts.

How to use this categorical data 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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