AP Statistics Five-Number Summary, Boxplots and Comparing Distributions Test Solutions and Scoring (PDF)

AP Statistics math test solutions: Five-Number Summary, Boxplots and Comparing Distributions – Maths PDF

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This boxplots compare test answers for AP Statistics covers five-number summary, boxplots and comparing distributions (Common Core AP STAT 1.8, AP STAT 1.9, HSS-ID.A.1, HSS-ID.A.2), with a free PDF to print.

Each solution includes a scoring guide. Award points for correct quartiles, a correct outlier decision, and a comparison that uses comparison words and the context of the data.

AP Statistics · Common Core State Standards: AP STAT 1.8, AP STAT 1.9, HSS-ID.A.1, HSS-ID.A.2

Boxplots compare test answers: worked solutions

Question 1 – Five-number summary [3 pts]

Median 24; \(Q_1=19\), \(Q_3=29\), \(IQR=10\), upper fence \(29+15=44\).

14, 19, 24, 29, 44; IQR 10; upper fence 44.

Scoring: 1 point for the five numbers, 1 point for IQR, 1 point for the fence.

Question 2 – Outlier decision [2 pts]

Boxplot of the delivery times.

The upper fence is \(29+1.5(10)=44\). The value 44 equals the fence, not beyond it.

44 is not an outlier under the 1.5 IQR rule, because it is not greater than 44.

Scoring: 1 point for the fence, 1 point for the correct conclusion.

Question 3 – Read a boxplot [3 pts]

Ages of customers.

(a) Range \(65-10=55\), IQR \(40-20=20\).

(b) The median is close to Q1 and the upper part is stretched, so the shape is skewed right.

55 and 20; skewed right; about 25%.

Scoring: 1 point per part.

Question 4 – Compare two stores [4 pts]

Medians: 18 and 19. IQRs: \(25-12=13\) and \(22-15=7\). Ranges: 28 and 20.

The centers are about the same (median 19 items per hour at Store 2, 18 at Store 1), but Store 1 is more variable (IQR 13 compared with 7, range 28 compared with 20).

Scoring: 1 point for each median, 1 point for IQR comparison, 1 point for a sentence with comparison words and context.

Question 5 – Percent in a section [2 pts]

Between Q1 and Q3: 50% of 200 = 100. Above the median: 50% = 100.

100 and 100.

Scoring: 1 point each.

Question 6 – Find a quartile [2 pts]

\(Q_3=30+14=44\). Upper fence: \(44+21=65\).

Q3 = 44; fence = 65.

Scoring: 1 point each.

Question 7 – Draw a boxplot [2 pts]

Boxplot of the summary.

\(IQR=26-12=14\). Fences are \(12-21=-9\) and \(26+21=47\), so there are no outliers.

IQR 14; no outliers.

Scoring: 1 point for a correct boxplot, 1 point for IQR 14.

Question 8 – Limits of a boxplot [2 pts]

A boxplot cannot show the number of peaks or gaps.

It hides bimodality or gaps; a histogram or dotplot shows them.

Scoring: 1 point for the feature, 1 point for a suitable graph.

Total score

Total

20 points

Key facts behind this boxplots compare test answers

Key facts

Five-number summary: minimum, Q1, median, Q3, maximum.
Each quarter of the ordered data holds about 25% of the values.
IQR = Q3 – Q1; outliers lie more than 1.5 IQR outside the box.
Compare center, spread, shape, and unusual features using comparison words.
Boxplots show skew and outliers but not the number of peaks.

How to use this boxplots compare 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.

All AP Statistics chapters: AP Statistics math.

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