Practice › Data Handling › Data Presentation and Interpretation

Data Presentation and Interpretation: Paper 1 Long Questions

Ten Paper 1 questions on organising and presenting data: reading and converting pie charts, bar charts, stem-and-leaf diagrams, histograms, frequency polygons, broken line graphs and scatter diagrams, spotting a misleading graph, and judging a sample. Mean, median and mode are left to the statistics sets. Answers sit under each question. Detailed solutions can be requested by email.

10 questions · about 60 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 2017 Paper 1 Q7 — changed: the total comes from the difference between two sectors, not from one sector's count

The pie chart shows the distribution of the favourite sports of the students in a school.

Pie chart of favourite sports: Basketball 120°, Football x°, Swimming 90°, Badminton 2x°, Others 30°

(a) Find $x$ . (1 mark)

(b) The number of students whose favourite sport is basketball is 60 more than the number whose favourite sport is football. Find the number of students in the school. (2 marks)

(c) Find the number of students whose favourite sport is badminton. (1 mark)

Show answer

(a) $x = 40$
(b) 270
(c) 60

Question 2 · Modelled on HKDSE 2021 Paper 1 Q9 — changed: the unknown bar is fixed by a comparison, and the chart is then converted into a pie chart

The bar chart shows the distribution of the numbers of books read by a group of students in a month. The number of students who read at least 2 books is 8 more than the number of students who read fewer than 2 books.

Bar chart of the numbers of books read: 0 books 6 students, 1 book k students, 2 books 12, 3 books 9, 4 books 3

(a) Find $k$ . (2 marks)

(b) If a student is randomly selected from the group, find the probability that the selected student read more than 2 books. (1 mark)

(c) The same data are presented in a pie chart. Find the angle of the sector representing the students who read 1 book. (1 mark)

Show answer

(a) $k = 10$
(b) $\frac{3}{10}$
(c) $9 0^{\circ}$

Question 3 · Modelled on HKDSE 2023 Paper 1 Q9 — changed: the stem-and-leaf data are reorganised into a grouped table instead of being averaged

The stem-and-leaf diagram shows the distribution of the scores (in marks) of 20 students in a quiz.

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

(a) Using the classes 30–39, 40–49, 50–59, 60–69 and 70–79, write down the frequency of each class. (2 marks)

(b) Write down the class boundaries and the class mark of the class 50–59. (2 marks)

(c) Find the percentage of students who scored at least 60 marks. (1 mark)

Show answer

(a) 3, 5, 6, 3, 3
(b) Class boundaries 49.5 and 59.5; class mark 54.5
(c) $30%$

Question 4 · New sub-type relative to recent papers — reading a histogram and building its frequency polygon, a junior-form skill that underpins every grouped-data question

The histogram shows the distribution of the heights (in cm) of the plants in a garden. The heights are recorded to the nearest cm.

Histogram of plant heights with class boundaries 10.5, 20.5, 30.5, 40.5, 50.5, 60.5 and frequencies 4, 9, 15, 8, 4

(a) Find the number of plants in the garden. (1 mark)

(b) Find the percentage of plants taller than 40.5 cm. (1 mark)

(c) A frequency polygon is drawn for the same distribution, starting and ending on the horizontal axis. Write down the coordinates of its highest point and of its two end points. (3 marks)

Show answer

(a) 40
(b) $30%$
(c) Highest point $(35.5, 15)$ ; end points $(5.5, 0)$ and $(65.5, 0)$

Question 5 · New sub-type — uses and abuses of statistics: a bar chart whose vertical axis does not start at zero

A company shows its annual sales in the bar chart below.

Bar chart of sales: 2024 is 500 and 2025 is 540 thousand units, vertical axis starting at 480

(a) Find the percentage increase in sales from 2024 to 2025. (1 mark)

(b) Find the ratio of the height of the bar for 2025 to the height of the bar for 2024, as drawn. (1 mark)

(c) A manager says, ‘The chart shows that our sales in 2025 were about three times those in 2024.’ Explain why the chart is misleading. (2 marks)

Show answer

(a) $8%$
(b) $3 : 1$
(c) The vertical axis starts at 480, not 0, so the bars show only the part above 480; the real increase is 8%, not 200%.

Question 6 · New sub-type — reading a broken line graph month by month and testing a claim about its trend

The broken line graph shows the number of visitors to a museum in the first six months of a year.

Broken line graph of museum visitors in thousands: Jan 12, Feb 15, Mar 11, Apr 18, May 24, Jun 21

(a) In which month was the increase in the number of visitors from the previous month the greatest? (1 mark)

(b) Find the percentage decrease in the number of visitors from May to June. (2 marks)

(c) A journalist writes, ‘The number of visitors rose every month from January to June.’ Is the journalist correct? Explain your answer. (1 mark)

Show answer

(a) April
(b) $12.5%$
(c) No. The number fell from February to March and from May to June.

Question 7 · Modelled on HKDSE 2013 Paper 2 Q28 (a scatter diagram) — turned into a long question that asks for a reading, an outlier and a description

The scatter diagram shows the numbers of hours of revision and the test scores of 11 students.

Scatter diagram of hours of revision against test score for 11 students

(a) Describe the relationship between the number of hours of revision and the test score. (1 mark)

(b) One point does not follow the general pattern. Write down its coordinates. (1 mark)

(c) How many students revised for more than 5 hours and scored more than 60 marks? (2 marks)

Show answer

(a) Positive linear correlation: more revision generally goes with a higher score.
(b) $(9, 35)$
(c) 3

Question 8 · Modelled on HKDSE 2022 Paper 1 Q9 — changed: the unknowns are fixed by a percentage condition, and the table is read as a histogram and a pie chart instead of being averaged

The frequency distribution table shows the travelling times to school of 40 students. It is given that

25%

of the students take more than 30.5 minutes.

Travelling time (minutes)	1–10	11–20	21–30	31–40	41–50
Number of students	6	$a$	13	$b$	4

(a) Find $a$ and $b$ . (2 marks)

(b) A histogram is drawn for the distribution. Write down the class boundaries of the class represented by the tallest bar. (2 marks)

(c) If the data are presented in a pie chart, find the angle of the sector representing the class 41–50. (1 mark)

Show answer

(a) $a = 11$ , $b = 6$
(b) 20.5 and 30.5 (the class 21–30)
(c) $3 6^{\circ}$

Question 9 · New sub-type — sampling: judging whether a sample represents the population, then estimating from a random sample

Tom wants to find out the favourite snacks of the 1200 students in his school. He asks the 50 members of the school basketball team.

(a) Explain why Tom's sample may not represent all the students in the school. (1 mark)

(b) Suggest a better way for Tom to choose 50 students. (1 mark)

(c) In a random sample of 60 students from the school, 18 choose fruit as their favourite snack. Estimate the number of students in the school whose favourite snack is fruit. (2 marks)

Show answer

(a) Basketball players are not typical of the whole school (for example, their eating habits may differ), so the sample is biased.
(b) Choose 50 students at random, for example by drawing 50 student numbers from all 1200.
(c) 360

Question 10 · Modelled on HKDSE 2013 Paper 2 Q30 (two pie charts) — changed: the two totals differ, so the sector angles alone cannot be compared

The pie charts show the distributions of the monthly expenditure of a family in 2024 and in 2025. The monthly expenditure was $20 000 in 2024 and $25 000 in 2025.

Two pie charts of a family's monthly expenditure. 2024: Food 108°, Rent 144°, Transport 36°, Others 72°. 2025: Food 90°, Rent 144°, Transport 36°, Others 90°

(a) Find the monthly expenditure on food in each year. (2 marks)

(b) Mary says, ‘The food sector is smaller in 2025, so the family spent less on food in 2025.’ Do you agree? Explain your answer. (1 mark)

(c) Find the percentage increase in the monthly expenditure on rent from 2024 to 2025. (2 marks)

Show answer

(a) $6000 in 2024 and $6250 in 2025
(b) No. A smaller sector of a larger total can be a larger amount: $6250 is more than $6000.
(c) $25%$

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

Where this sits in the syllabus

Data presentation is taught in the junior forms, but HKDSE Paper 1 still opens most statistics questions with a pie chart, bar chart, stem-and-leaf diagram or frequency table. Most marks are lost on reading, not calculating: a sector angle taken as a count, or a class limit used where a class boundary is needed.

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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