Practice › Data Handling › Data Presentation and Interpretation

Data Presentation and Interpretation: Paper 2 Challenge MC

Challenge tier. Each question has a distractor that is the right number to the wrong question: a sector read as an amount, a boundary for ages, percentage changes read as sales, a total that changes when members join. Work the standard Paper 2 set first. Answers sit under each question. Detailed solutions can be requested by email.

10 questions · about 20 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 · Challenge — states a condition, not a method: the sectors come only as a ratio

In a pie chart, the angles of the sectors A, B, C and D are in the ratio

2 : 3 : 4 : 6

. There are 36 more people in group D than in group A. Find the total number of people.

Show answer

B. D − A is $\frac{4}{15}$ of the total, so the total is $36 \times \frac{15}{4} = 135$ .

Question 2 · Challenge — a genuine trap: the order of the leaves restricts the unknown digit from below as well as above

In the stem-and-leaf diagram below,

a

is a digit and the leaves are arranged in ascending order. Exactly 6 of the values are less than 36. How many possible values of

a

are there?

Stem (tens)	Leaf (units)
2	1 4 7
3	0 2 $a$ 8
4	1 5 5

Show answer

C. $30 + a < 36$ needs $a \leq 5$ , and the ordering needs $2 \leq a \leq 8$ , so $a = 2, 3, 4, 5$ . Ignoring the ordering gives 6.

Question 3 · Challenge — options that reward the second check: which facts about a frequency polygon really hold

A histogram with equal class widths and its frequency polygon are drawn for the same distribution. The polygon starts and ends on the horizontal axis. Which of the following must be true?
I. The area under the frequency polygon equals the total area of the bars of the histogram.
II. The highest point of the polygon lies directly above the upper class boundary of the class with the greatest frequency.
III. The polygon meets the horizontal axis at the class marks of two empty classes, one at each end.

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

Show answer

C. The polygon joins points above the class marks, so II is false. The triangles cut off and added balance exactly, which is why I is true.

Question 4 · Challenge — a genuine trap: for ages, the class boundaries are not the usual half-units

The ages (in completed years) of some people are grouped into classes 10–14, 15–19, 20–24, …. What is the upper class boundary of the class 10–14?

14
14.5
14.99
15

Show answer

D. Ages are truncated, not rounded: a person aged 14 can be up to just under 15 years old, so the boundary is 15.

Question 5 · Challenge — runs the truncated-axis question backwards: recover where the axis starts

A bar chart shows sales of 500 units in 2024 and 560 units in 2025. As drawn, the bar for 2025 is 4 times as tall as the bar for 2024, because the vertical axis does not start at 0. At what value does the vertical axis start?

Show answer

C. If the axis starts at $s$ , then $560 - s = 4 (500 - s)$ , which gives $s = 480$ .

Question 6 · Challenge — a genuine trap: a smaller sector of a larger total

A company's total expenses were $2.4 million in 2024 and $3 million in 2025. In the pie charts of the expenses, the salary sector is

15 0^{\circ}

in 2024 and

12 6^{\circ}

in 2025. Which of the following describes the change in salary expenses?

Decreased by $16%$
Decreased by $4%$
Unchanged
Increased by $5%$

Show answer

D. $1.0 million in 2024 and $1.05 million in 2025: up $5%$ . $16%$ is the change in the angle only.

Question 7 · Challenge — more justify and explain: what a scatter diagram can and cannot show

Which of the following is/are true?
I. If a scatter diagram shows a strong positive correlation between

x

and

y

, then an increase in

x

causes an increase in

y

.
II. If all the points of a scatter diagram lie on a straight line with a negative slope, then

x

and

y

have a negative correlation.
III. If a scatter diagram shows no linear correlation, then

x

and

y

are not related in any way.

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

Show answer

A. Correlation is not causation (I), and points on a curve can show no linear correlation yet be closely related (III).

Question 8 · Challenge — a genuine trap: new members change the total as well as the sector

A pie chart shows the distribution of the 180 members of a club. The sector for group C is

6 0^{\circ}

. Some new members join group C only, and the sector for group C becomes

9 0^{\circ}

. How many new members joined?

Show answer

D. $\frac{30 + n}{180 + n} = \frac{1}{4}$ gives $n = 20$ . 15 is what you get if the total is kept at 180.

Question 9 · Challenge — a genuine trap: the graph shows percentage changes, not sales

The broken line graph shows the percentage change in the sales of a shop in each quarter, compared with the previous quarter. Which of the following must be true?
I. The sales in Q3 were lower than those in Q2.
II. The sales in Q4 were lower than those in Q3.
III. The sales in Q3 were higher than those in Q1.

Broken line graph of percentage change in sales compared with the previous quarter: Q2 +20%, Q3 −10%, Q4 +5%

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

Show answer

B. Q4 rose by 5% on Q3, so II is false. Q3 is $1.2 \times 0.9 = 1.08$ times Q1, so III is true.

Question 10 · Challenge — a genuine trap: data recorded to one decimal place move the class boundaries to the second decimal place

The weights (in kg) of some parcels are recorded correct to 1 decimal place and grouped into the classes 50.0–54.9, 55.0–59.9, …. Find the class mark of the class 55.0–59.9.

57.45
57.5
57.95
58

Show answer

A. The class boundaries are 54.95 and 59.95, so the class mark is $\frac{54.95 + 59.95}{2} = 57.45$ .

Continue practising this topic: Try the Paper 2 multiple-choice to build the basics, or move to Paper 1 long questions — also available as Paper 1 Challenge.

Where this sits in the syllabus

The harder Paper 2 questions on this topic rarely need long working. They test whether you notice what a chart actually shows: a percentage change rather than a value, a truncated axis, or a total that changes when new data arrive.

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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