Data Handling: Mathematics Darjah 5 questions

Section A: objective questions

10 marks

Choose the correct answer.

Which word means the value that appears most often in a set of data?

Range
Median
Mode
Mean

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The mode is the value with the highest frequency. The range is the difference between the biggest and smallest values, the median is the middle value and the mean is the average.

For the teacher: Remembering, low difficulty, standard 8.2.1

Textbook p. 254

What is the range of the data 14, 9, 21, 12, 17?

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Range = maximum value − minimum value = 21 − 9 = 12.

For the teacher: Remembering, low difficulty, standard 8.2.1

Textbook p. 254

Diagram 1 shows how pupils go to school. What is the percentage of pupils who walk?

Pie chart: Bus 45%, Car 30%, Bicycle 15%, Walking unknown — Diagram 1

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A pie chart totals 100%. 45% + 30% + 15% = 90%, so walking is 100% − 90% = 10%.

For the teacher: Understanding, low difficulty, standard 8.1.1

Textbook p. 251

What is the mean of 6, 8, 9, 5 and 12?

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Total = 6 + 8 + 9 + 5 + 12 = 40. Mean = 40 ÷ 5 = 8. (40 is the total, not the mean.)

For the teacher: Applying, low difficulty, standard 8.2.1

Textbook p. 255

What is the median of 12, 7, 15, 9, 10 and 20?

10
12
11
13.5

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In order: 7, 9, 10, 12, 15, 20. There are 6 values, so the median is the mean of the 3rd and 4th values: (10 + 12) ÷ 2 = 11.

For the teacher: Applying, medium difficulty, standard 8.2.1

Textbook p. 256

Diagram 2 shows the favourite sports of 200 pupils. How many pupils like hockey?

Pie chart of 200 pupils: Football 40%, Badminton 25%, Swimming 20%, Hockey 15% — Diagram 2

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15% of 200 = 15 ÷ 100 × 200 = 30 pupils. (15 is the percentage, not the number of pupils.)

For the teacher: Applying, low difficulty, standard 8.1.1

Textbook p. 252

The bar chart in Diagram 3 shows the number of books read by 12 pupils in a month. What is the mode?

Bar chart: 1 book 3 pupils, 2 books 6 pupils, 3 books 2 pupils, 4 books 1 pupil — Diagram 3

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The tallest bar is for 2 books, with 6 pupils. The mode is the value 2 books, not the frequency 6.

For the teacher: Understanding, low difficulty, standard 8.2.1

Textbook p. 256

The table shows the number of goals scored by 10 pupils in a game.

Goals	1	2	3	4
Number of pupils	2	4	3	1

What is the mean number of goals?

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Total goals = 1×2 + 2×4 + 3×3 + 4×1 = 2 + 8 + 9 + 4 = 23. Mean = 23 ÷ 10 = 2.3.

For the teacher: Applying, medium difficulty, standard 8.2.1

Textbook p. 256

The mean of five numbers is 11. Four of the numbers are 10, 14, 9 and 15. What is the fifth number?

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Total of five numbers = 5 × 11 = 55. The four numbers add up to 10 + 14 + 9 + 15 = 48. The fifth number is 55 − 48 = 7.

For the teacher: Analysing, medium difficulty, standard 8.3.1

Textbook p. 261

The data 4, 7, 7, 8, 9 has a new value, 10, added to it. Which one of these does not change?

Mode
Median
Mean
Range

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The mode stays 7. The median changes from 7 to 7.5, the mean from 7 to 7.5 (45 ÷ 6), and the range from 5 to 6.

For the teacher: Analysing, high difficulty, standard 8.2.1

Textbook p. 256

Section B: structured questions

33 marks

Answer all questions. Show your working.

The numbers of goals scored by a team in seven matches are: 8, 11, 8, 14, 9, 8, 12.

[1 mark] (a)What is the frequency of 8?

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3 [1]1

Tick each point you got.

[1 mark] (b)State the mode.

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8 [1]1

Tick each point you got.

[1 mark] (c)State the range.

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14 − 8 = 6 [1]1

Tick each point you got.

For the teacher: Remembering, low difficulty, standard 8.2.1

Textbook p. 254

Diagram 4 shows how 80 pupils spend their free time.

Pie chart of 80 pupils: Reading 30%, Football 25%, Drawing 20%, Chess 15%, Cycling unknown — Diagram 4

[1 mark] (a)What is the percentage of pupils who like cycling?

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100% − (30% + 25% + 20% + 15%) = 10% [1]1

Tick each point you got.

[2 marks] (b)How many pupils like the most popular activity?

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Reading is the highest, 30% [1]1
30 ÷ 100 × 80 = 24 pupils [1]1

Tick each point you got.

[1 mark] (c)Find the difference in the number of pupils between drawing and chess.

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(20% − 15%) = 5%; 5 ÷ 100 × 80 = 4 pupils [1]1

Tick each point you got.

For the teacher: Understanding, low difficulty, standard 8.1.1

Textbook p. 252

The bar chart in Diagram 5 shows the weekly savings of 10 pupils.

Bar chart of weekly savings of 10 pupils: RM2 two pupils, RM3 four pupils, RM4 three pupils, RM5 one pupil — Diagram 5

[1 mark] (a)State the mode.

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RM3 [1]1

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[1 mark] (b)Calculate the range.

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RM5 − RM2 = RM3 [1]1

Tick each point you got.

[2 marks] (c)Find the median.

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In order: 2, 2, 3, 3, 3, 3, 4, 4, 4, 5; the 5th and 6th values are 3 and 3 [1]1
Median = RM3 [1]1

Tick each point you got.

[2 marks] (d)Calculate the mean.

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(2 × 2) + (4 × 3) + (3 × 4) + (1 × 5) = 33 [1]1
33 ÷ 10 = RM3.30 [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 8.2.1

Textbook p. 256

The pictograph in Diagram 6 shows the time some pupils practise the piano each day.

Pictograph: 20 minutes one symbol, 25 minutes two symbols, 30 minutes one symbol, 35 minutes one symbol; each symbol represents 2 pupils — Diagram 6

[1 mark] (a)How many pupils practise for 25 minutes?

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2 × 2 = 4 pupils [1]1

Tick each point you got.

[2 marks] (b)State the mode and the range.

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Mode = 25 minutes [1]1
Range = 35 − 20 = 15 minutes [1]1

Tick each point you got.

[2 marks] (c)Calculate the mean time.

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Total = 2×20 + 4×25 + 2×30 + 2×35 = 270 minutes; 10 pupils [1]1
270 ÷ 10 = 27 minutes [1]1

Tick each point you got.

For the teacher: Applying, low difficulty, standard 8.2.1

Textbook p. 255

The pie chart in Diagram 7 shows the mass of newspapers gathered by 10 pupils for recycling.

Pie chart of 10 pupils: 5 kg 10%, 6 kg 40%, 7 kg 30%, 8 kg 20% — Diagram 7

[1 mark] (a)How many pupils gathered 7 kg?

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30 ÷ 100 × 10 = 3 pupils [1]1

Tick each point you got.

[1 mark] (b)State the mode.

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6 kg [1]1

Tick each point you got.

[1 mark] (c)Find the median.

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Data (1, 4, 3, 2 pupils): 5, 6, 6, 6, 6, 7, 7, 7, 8, 8; (6 + 7) ÷ 2 = 6.5 kg [1]1

Tick each point you got.

[2 marks] (d)Calculate the mean mass.

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(1 × 5) + (4 × 6) + (3 × 7) + (2 × 8) = 66 [1]1
66 ÷ 10 = 6.6 kg [1]1

Tick each point you got.

For the teacher: Applying, medium difficulty, standard 8.2.1

Textbook p. 257

Aini scored 72, 85, 90 and 77 marks in four Mathematics tests.

[2 marks] (a)Calculate her mean mark.

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72 + 85 + 90 + 77 = 324 [1]1
324 ÷ 4 = 81 [1]1

Tick each point you got.

[2 marks] (b)She wants a mean of 84 after the fifth test. What mark must she score in the fifth test?

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Total needed = 5 × 84 = 420 [1]1
420 − 324 = 96 marks [1]1

Tick each point you got.

For the teacher: Analysing, medium difficulty, standard 8.3.1

Textbook p. 261

The table shows the number of brothers and sisters of 10 pupils.

Number of brothers and sisters	1	2	3	4
Number of pupils	4	2	3	1

Hana says, "The median is 1, because 1 has the highest frequency."

[1 mark] (a)State the mode.

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1 [1]1

Tick each point you got.

[2 marks] (b)Is Hana correct? Prove it.

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No [1]1
In order: 1, 1, 1, 1, 2, 2, 3, 3, 3, 4; the 5th and 6th values are 2 and 2, so the median is 2. Hana has found the mode, not the median [1]1

Tick each point you got.

For the teacher: Evaluating, high difficulty, standard 8.3.1

Textbook p. 262

Write a set of five numbers with a mode of 4, a median of 5 and a range of 6.

[3 marks] (a)Write your five numbers and show that they fit.

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Two or more 4s, so the mode is 4 [1]1
Middle value of the five numbers in order is 5 [1]1
Largest − smallest = 6 [1]. Example: 4, 4, 5, 7, 10 (10 − 4 = 6)1

Tick each point you got.

For the teacher: Creating, high difficulty, standard 8.2.1

Textbook p. 255

Section A: objective questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Section B: structured questions

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18