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Data Presentation and Interpretation: Paper 2 Multiple-Choice

Ten Paper 2 multiple-choice questions on reading data displays quickly and accurately: sector angles, bar heights, leaves in a range, class boundaries and class marks, frequency polygons, correlation, a truncated axis and random sampling. Answers sit under each question. Detailed solutions can be requested by email.

10 questions · about 15 minutes · answers below each question

All questions are original, written for Math and AI Academy and modelled on past-paper style. They are not reproductions of HKEAA examination questions.

Question 1 · Modelled on HKDSE 2014 Paper 2 Q29 — changed: the known sector is food, and the ratio of two angles gives the answer

The pie chart shows the distribution of Mary's expenditure in a month. She spends $1800 on food that month. Find her expenditure on transport that month.

Pie chart of Mary's monthly expenditure: Food 144°, Transport 60°, Entertainment 48°, Others 108°

$540
$750
$900
$1080

Show answer

B. Transport is $\frac{60}{144}$ of food: $\frac{60}{144} \times 1800 = 750$ .

Question 2 · Modelled on HKDSE 2017 Paper 2 Q28 — changed: a percentage of matches instead of a probability

The bar chart shows the distribution of the numbers of goals scored by a football team in its matches in a season. In what percentage of the matches did the team score at least 2 goals?

Bar chart of goals scored per match: 0 goals 4 matches, 1 goal 7, 2 goals 6, 3 goals 2, 4 goals 1

$20%$
$35%$
$45%$
$55%$

Show answer

C. $6 + 2 + 1 = 9$ of the 20 matches, which is $45%$ . $55%$ counts fewer than 2 goals instead.

Question 3 · Modelled on HKDSE 2012 Paper 2 Q28 — changed: counting within a closed range instead of averaging

The stem-and-leaf diagram shows the distribution of the heights (in cm) of some plants. How many plants are at least 25 cm but not more than 40 cm tall?

Stem (tens)	Leaf (units)
1	4 6 9
2	0 3 5 5 8
3	1 2 2 7 9
4	0 3 6 8

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D. 25, 25, 28, 31, 32, 32, 37, 39 and 40: nine plants. Leaving out 40 gives the trap answer 8.

Question 4 · New sub-type — class mark, class boundaries and class width of a grouped class

The lengths of some leaves are measured to the nearest cm and grouped into classes. Consider the class 25–29 (cm). Which of the following are true?
I. The class mark is 27 cm.
II. The lower class boundary is 24.5 cm.
III. The class width is 4 cm.

I only
I and II only
I and III only
I, II and III

Show answer

B. The boundaries are 24.5 and 29.5, so the width is 5 cm, not 4 cm.

Question 5 · New sub-type — reading a histogram through its class boundaries

The histogram shows the distribution of the weights of 50 parcels. Find the percentage of parcels weighing more than 15.5 kg.

Histogram of parcel weights with boundaries 0.5, 5.5, 10.5, 15.5, 20.5, 25.5 and frequencies 5, 12, 15, 10, 8

$36%$
$46%$
$64%$
$66%$

Show answer

A. $10 + 8 = 18$ of 50 parcels, which is $36%$ .

Question 6 · New sub-type — the points that make up a frequency polygon

A frequency polygon is drawn for the distribution in the table, starting and ending on the horizontal axis. Which of the following points does NOT lie on the frequency polygon?

Mark	10–19	20–29	30–39	40–49
Frequency	3	7	10	5

$(14.5, 3)$
$(24.5, 7)$
$(35, 10)$
$(54.5, 0)$

Show answer

C. Points are plotted at class marks; the class mark of 30–39 is 34.5, not 35. $(54.5, 0)$ is the right-hand end point.

Question 7 · Modelled on HKDSE 2013 Paper 2 Q28 — changed: describe the correlation rather than match a formula

Which of the following best describes the relationship between

x

and

y

shown in the scatter diagram?

Scatter diagram in which y decreases steadily as x increases, points close to a straight line

Strong positive linear correlation
No correlation
Weak positive linear correlation
Strong negative linear correlation

Show answer

D. As $x$ increases, $y$ decreases, and the points lie close to a straight line.

Question 8 · New sub-type — uses and abuses of statistics: the visual effect of a truncated axis

A bar chart shows that a shop sold 820 items in 2024 and 860 items in 2025. The vertical axis of the chart starts at 800. As drawn, the bar for 2025 is

k

times as tall as the bar for 2024. Find

k

Show answer

A. The bars show $820 - 800 = 20$ and $860 - 800 = 60$ , so $k = 3$ , although sales rose by under 5%.

Question 9 · New sub-type — sampling: recognising a random sample

A school wants to choose 30 of its students to find out how long students spend on homework. Which of the following methods gives a random sample?

Asking the first 30 students who arrive at school one morning
Asking 30 students who are studying in the library
Asking 30 students who volunteer on the school website
Drawing 30 numbers from a box containing the student numbers of all students

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D. Only drawing numbers gives every student the same chance of being chosen; the others favour particular groups.

Question 10 · Modelled on HKDSE 2013 Paper 2 Q30 — changed: new angles, and the statement that must be true is about proportions, not amounts

The pie charts show the distributions of the profits of shop X and shop Y from selling stationery in a certain month. Which of the following must be true?

Two pie charts of profits. Shop X: Pens 120°, Pencils 90°, Notebooks 100°, Rulers 50°. Shop Y: Pens 100°, Pencils 90°, Notebooks 110°, Rulers 60°

The profit from pencils of shop X equals that of shop Y.
In both shops, pencils account for 25% of the profit.
In shop X, the profit from pens is greater than the total profit from pencils and rulers.
The profit from notebooks of shop Y is greater than that of shop X.

Show answer

B. $9 0^{\circ}$ is one quarter of $36 0^{\circ}$ in both charts. The total profits are not given, so the amounts cannot be compared.

Continue practising this topic: Try the Paper 2 Challenge MC for harder variants, or move to Paper 1 long questions — also available as Paper 1 Challenge.

Where this sits in the syllabus

In Paper 2 a data-display question should take about a minute. The speed comes from knowing exactly where to read: angles in proportion to frequencies, class marks for polygons, class boundaries for histograms.

Full coverage of this topic, and the rest of the course, is on the Mathematics page. More sets are listed on the practice index.

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