Mathematics questions, chapter 12

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Data handling

40 marks. Use Practice to check each answer as you go, or Exam to answer everything first. You may use a calculator. Show your working for Section B.

Section A: objective questions

12 marks

Choose the correct answer.

Question 1

Which of the following is a statistical question?

"How tall is Rosmee?"
"How many pages are there in this textbook?"
"How many hours do Form 1 students spend on homework each week?"
"What is the capital city of Malaysia?"

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A statistical question is answered by collecting data that varies. The hours spent on homework are different for different students. The other questions each have only one answer.

For the teacher: Remembering, low difficulty, standard 12.1.1

Textbook p. 266

Question 2

Which of the following is categorical data?

The blood groups of the students in a class
The masses of the students in a class
The number of siblings of each student
The time each student spends exercising

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Blood group (A, B, O, AB) is a characteristic that cannot be measured with numbers. Mass, number of siblings and time are all measured or counted, so they are numerical.

For the teacher: Understanding, low difficulty, standard 12.1.2

Textbook p. 267

Question 3

Which of the following is continuous numerical data?

The number of goals scored in a match
The colours of cars in a car park
The number of books borrowed from the library
The time taken to run 100 m

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Time is measured on a continuous scale (for example 13.4 s). Goals and books are counted in whole units, so they are discrete. Colours are categorical.

For the teacher: Understanding, medium difficulty, standard 12.1.2

Textbook p. 267

Question 4

The data shows the number of goals scored by a football team in 15 matches.
2, 0, 1, 3, 1, 2, 2, 4, 1, 0, 2, 3, 2, 1, 2
In a frequency table, what is the frequency of 2 goals?

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Tally every 2 in the list: there are 6 of them. 4 is the frequency of 1 goal, and 15 is the total number of matches.

For the teacher: Applying, low difficulty, standard 12.1.2

Textbook p. 268

Question 5

In a survey of 40 students, 12 students chose badminton as their favourite sport. Find the angle of the sector for badminton in a pie chart.

108°
12°
30°
120°

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Angle = 12/40 × 360° = 108°. 30 is the percentage (30%), not the angle, and 12° uses the frequency as the angle.

For the teacher: Applying, medium difficulty, standard 12.1.3

Textbook p. 271

Question 6

Diagram 1 shows the points scored by 17 basketball players. Find the difference between the highest and the lowest points.

Stem-and-leaf plot Points Scored by Players. 2 | 3 5 8; 3 | 0 2 2 6 9; 4 | 1 4 4 4 7 8; 5 | 0 3 6. Key 2 | 3 means 23 points — Diagram 1

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Highest = 56, lowest = 23, so the difference is 56 − 23 = 33. 30 compares only the stems (50 − 20), and 3 compares only the leaves (6 − 3).

For the teacher: Applying, low difficulty, standard 12.1.5

Textbook p. 281

Question 7

Puan Aini records the temperature in her classroom every hour from 8 a.m. to 2 p.m. Which representation is the most suitable to show how the temperature changes?

Pie chart
Line graph
Stem-and-leaf plot
Dot plot

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A line graph shows changes in data over a period of time. A pie chart shows parts of a whole, which makes no sense for temperatures.

For the teacher: Understanding, medium difficulty, standard 12.1.3

Textbook p. 271

Question 8

Diagram 2 is a dot plot of the number of books read in a month by 20 students. What percentage of the students read at least 4 books?

Dot plot Books Read in a Month: 0 books 1 dot, 1 book 3 dots, 2 books 5 dots, 3 books 4 dots, 4 books 4 dots, 5 books 2 dots, 6 books 1 dot — Diagram 2

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At least 4 means 4, 5 or 6 books: 4 + 2 + 1 = 7 students. 7/20 × 100% = 35%. 20% counts only the students who read exactly 4 books, and 7% forgets to divide by 20.

For the teacher: Applying, medium difficulty, standard 12.1.5

Textbook p. 278

Question 9

Diagram 3 shows the Science test marks of 60 students. How many students scored more than 70 marks?

Histogram Science Test Marks: 41-50 6 students, 51-60 12, 61-70 20, 71-80 15, 81-90 7 — Diagram 3

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More than 70 marks means the classes 71–80 and 81–90: 15 + 7 = 22. 15 uses only one class, and 42 wrongly includes 61–70.

For the teacher: Analysing, medium difficulty, standard 12.1.5

Textbook p. 279

Question 10

Diagram 4 shows the number of visitors to a museum from Monday to Friday. How many more visitors came on Friday than on Tuesday?

Bar chart Visitors to a Museum: Monday 40, Tuesday 25, Wednesday 50, Thursday 35, Friday 65 — Diagram 4

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Friday = 65 and Tuesday = 25, so 65 − 25 = 40 more visitors. 90 adds the two days instead of subtracting.

For the teacher: Applying, low difficulty, standard 12.1.5

Textbook p. 277

Question 11

Diagram 5 is a frequency polygon of the time taken by a group of pupils to finish a puzzle. How many pupils took 16 minutes or more?

Frequency polygon Time to Finish a Puzzle: 1-5 0, 6-10 5, 11-15 9, 16-20 14, 21-25 8, 26-30 4, 31-35 0 — Diagram 5

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16 minutes or more means the classes 16–20, 21–25 and 26–30: 14 + 8 + 4 = 26. 14 uses only the 16–20 class, 12 starts from 21 minutes, and 40 is all the pupils.

For the teacher: Analysing, high difficulty, standard 12.1.5

Textbook p. 280

Question 12

Diagram 6 shows a pie chart drawn by Kamal for the favourite sports of his classmates. Which statement best evaluates his pie chart?

Pie chart Favourite Sports: Football 40%, Badminton 25%, Hockey 20%, Swimming 20% — Diagram 6

It is accurate because football has the largest sector.
It is not accurate because the percentages add up to 105%, not 100%.
It is not accurate because a pie chart cannot show percentages.
It is accurate because hockey and swimming have equal sectors.

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40 + 25 + 20 + 20 = 105%. The parts of a whole must add up to 100%, so the data shown is not accurate. Pie charts can show percentages.

For the teacher: Evaluating, medium difficulty, standard 12.1.6

Textbook p. 282

Section B: structured questions

28 marks

Answer all questions. Show your working.

Question 13

Siti collects four kinds of data about her classmates: (i) favourite colour, (ii) length of their hand span, (iii) mode of transport to school, (iv) number of siblings.

[2 marks] (a)Classify each kind of data as categorical or numerical.

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(i) categorical, (ii) numerical, (iii) categorical, (iv) numerical: all four correct [2]; two or three correct [1]2

Tick each point you got.

[1 mark] (b)The number of siblings is

Adiscrete dataBcontinuous data

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discrete data

Siblings are counted in whole numbers (0, 1, 2, …), so the data is discrete.

For the teacher: Remembering, low difficulty, standard 12.1.2

Textbook p. 267

Question 14

Diagram 7 shows the number of books read by 24 students in a month.

Data card: 2 1 3 0 2 4 1 2 / 3 2 1 0 3 2 2 4 / 1 3 2 1 0 2 3 1 — Diagram 7

[2 marks] (a)Construct a frequency table, with tally marks, for the data.

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Table with the values 0, 1, 2, 3, 4 and tally marks [1]1
Frequencies 0 books: 3, 1 book: 6, 2 books: 8, 3 books: 5, 4 books: 2 (total 24) [1]1

Tick each point you got.

[1 mark] (b)How many students read more than 2 books?

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5 + 2 = 7 students [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 12.1.2

Textbook p. 268

Question 15

Diagram 8 is a pie chart showing how 72 students travel to school.

Pie chart Transport to School: Car 100 degrees, School bus 120 degrees, Bicycle 60 degrees, Walk x — Diagram 8

[2 marks] (a)Find the value of x.

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x = 360° − 100° − 120° − 60° [1]1
x = 80° [1]1

Tick each point you got.

[2 marks] (b)Find the number of students who travel by school bus.

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120/360 × 72 [1]1
= 24 students [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 12.1.3

Textbook p. 271

Question 16

Diagram 9 shows the mass of paper collected for recycling by a school from January to June.

Line graph Paper Collected for Recycling: January 40 kg, February 55, March 50, April 65, May 70, June 80 — Diagram 9

[1 mark] (a)In which month did the mass of paper collected decrease compared with the month before?

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March (from 55 kg to 50 kg) [1]1

Tick each point you got.

[2 marks] (b)Find the mean mass of paper collected per month over the six months.

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Total = 40 + 55 + 50 + 65 + 70 + 80 = 360 kg [1]1
Mean = 360 ÷ 6 = 60 kg [1]1

Tick each point you got.

[1 mark] (c)Based on the trend of the graph, predict the mass of paper collected in July.

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Any value from 85 kg to 95 kg, because the mass is increasing [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 12.1.5

Textbook p. 277

Question 17

Diagram 10 shows the time taken by 25 students to complete a cross-country run.

Stem-and-leaf plot Time for a Cross-country Run: 2 | 4 6 8; 3 | 0 1 3 5 5 7 9; 4 | 0 2 2 2 4 6 8 8; 5 | 1 3 5 7; 6 | 0 4 6. Key 2 | 4 means 24 minutes — Diagram 10

[1 mark] (a)State the shortest time and the longest time.

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Shortest 24 minutes and longest 66 minutes [1]1

Tick each point you got.

[2 marks] (b)Students who finish in less than 35 minutes receive a medal. Find the percentage of students who receive a medal.

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Less than 35 minutes: 24, 26, 28, 30, 31, 33 = 6 students [1]1
6/25 × 100% = 24% [1]1

Tick each point you got.

[1 mark] (c)State one inference based on the stem-and-leaf plot.

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Most students took 30 to 49 minutes (15 of the 25 students) [1]1

Tick each point you got.

For the teacher: Analysing, high difficulty, standard 12.1.5

Textbook p. 281

Question 18

Diagram 11 shows the blood groups of 50 blood donors.

Pie chart Blood Groups of 50 Donors: A 30%, B 24%, O 36%, AB 10% — Diagram 11

[2 marks] (a)Find the number of donors in each blood group.

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Method: percentage × 50, e.g. 30/100 × 50 [1]1
A = 15, B = 12, O = 18, AB = 5 [1]1

Tick each point you got.

[1 mark] (b)The pie chart is to be converted to another representation that shows the actual number of donors in each group. Name a suitable representation and justify your choice.

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Bar chart, because it shows and compares the number of donors in each blood group [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 12.1.4

Textbook p. 277

Question 19

Diagram 12 shows the number of lamps sold by five shops in a month. Shop E claims, "We sold twice as many lamps as Shop C, look at the bars!"

Bar chart Lamp Sales with the vertical axis starting at 100: A 150, B 130, C 120, D 145, E 140 — Diagram 12

[1 mark] (a)State the number of lamps sold by Shop C and by Shop E.

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C = 120 and E = 140 [1]1

Tick each point you got.

[2 marks] (b)Is Shop E's claim valid? Show your working.

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Twice Shop C = 2 × 120 = 240 (or E − C = 140 − 120 = 20) [1]1
Not valid: 140 is not 240; E sold only 20 more lamps than C [1]1

Tick each point you got.

[1 mark] (c)Explain why the bar chart makes the claim look true, and how it should be drawn.

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The vertical axis starts at 100, so bar E (40 units) looks twice bar C (20 units); the scale should start at 0 [1]1

Tick each point you got.

For the teacher: Evaluating, high difficulty, standard 12.1.6

Textbook p. 285

Question 20

Aina wants to find out how much time the Form 1 students in her school spend on the Internet each day. She plans to survey 30 students and record each time to the nearest minute.

[1 mark] (a)Write a statistical question for Aina's study.

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A question whose answers vary, e.g. "How many minutes do the Form 1 students spend on the Internet each day?" [1]1

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[1 mark] (b)Suggest a suitable method to collect the data.

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Survey with a questionnaire (or interview) [1]1

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[1 mark] (c)Choose a stem-and-leaf plot or a pie chart to represent her data. Justify your choice.

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Stem-and-leaf plot, because the data is numerical and the plot shows the distribution while keeping every original value [1]1

Tick each point you got.

For the teacher: Creating, high difficulty, standard 12.1.1

Textbook p. 266

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