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Primary 6 PSLE Mathematics Data Analysis Quiz

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Primary 6 PSLE Mathematics Quiz - Data Analysis

Name: ___________________________
Class: Primary 6 _______
Date: ___________________________
Score: _______ / 50

Duration: 45 minutes
Total Marks: 50

Instructions:

Answer all questions.
Show your working clearly in the space provided.
Write your answers in the spaces provided.
For questions requiring units, give your answers in the units stated.
The number of marks is given in brackets [ ] at the end of each question or part question.

Section A: Multiple Choice Questions (Questions 1–5, 2 marks each)

1. The bar graph below shows the number of books read by five students in a month.

<image_placeholder> id: Q1-fig1 type: bar_graph linked_question: Q1 description: Vertical bar graph showing books read by 5 students labels: Students: Ali, Ben, Cindy, Devi, Eli; Y-axis: Number of books (scale 0-30, intervals of 5) values: Ali: 15, Ben: 22, Cindy: 18, Devi: 25, Eli: 10 must_show: All 5 bars with correct heights, labelled axes, title "Books Read in a Month" </image_placeholder>

What is the average number of books read by the five students?

[ ] A. 16
[ ] B. 18
[ ] C. 20
[ ] D. 22

Answer: _______ [2]

2. The pie chart shows the favourite fruits of 200 students.

<image_placeholder> id: Q2-fig1 type: pie_chart linked_question: Q2 description: Pie chart showing favourite fruits of 200 students labels: Apples (90°), Oranges (72°), Bananas (108°), Grapes (90°) values: Total students = 200 must_show: Four sectors with correct angles, legend, title "Favourite Fruits of 200 Students" </image_placeholder>

How many students chose bananas as their favourite fruit?

[ ] A. 40
[ ] B. 50
[ ] C. 60
[ ] D. 70

Answer: _______ [2]

3. The table below shows the number of goals scored by a football team in 10 matches.

Goals Scored	0	1	2	3	4
Frequency	1	3	2	3	1

What is the mode of the number of goals scored?

[ ] A. 1
[ ] B. 2
[ ] C. 1 and 3
[ ] D. 3

Answer: _______ [2]

4. The line graph shows the temperature recorded at different times of a day.

<image_placeholder> id: Q4-fig1 type: line_graph linked_question: Q4 description: Line graph showing temperature changes throughout a day labels: X-axis: Time (6am, 9am, 12pm, 3pm, 6pm, 9pm); Y-axis: Temperature (°C) from 20°C to 35°C values: 6am: 22°C, 9am: 26°C, 12pm: 32°C, 3pm: 34°C, 6pm: 30°C, 9pm: 24°C must_show: Points plotted and connected with line segments, labelled axes, title "Temperature Changes in a Day" </image_placeholder>

Between which two times did the temperature increase the most?

[ ] A. 6am to 9am
[ ] B. 9am to 12pm
[ ] C. 12pm to 3pm
[ ] D. 3pm to 6pm

Answer: _______ [2]

5. The average of 6 numbers is 24. When one number is removed, the average of the remaining 5 numbers becomes 22. What is the number that was removed?

[ ] A. 30
[ ] B. 32
[ ] C. 34
[ ] D. 36

Answer: _______ [2]

Section B: Short Answer Questions (Questions 6–15, 3 marks each)

6. The table shows the number of storybooks borrowed by pupils in a class in a week.

Number of Books	0	1	2	3	4
Number of Pupils	4	8	6	5	2

(a) How many pupils are there in the class?
Answer: _______ [1]

(b) Find the total number of books borrowed.
Answer: _______ [1]

(c) What is the average number of books borrowed per pupil? Give your answer correct to 1 decimal place.
Answer: _______ [1]

7. The bar graph below shows the number of visitors to a museum from Monday to Friday.

<image_placeholder> id: Q7-fig1 type: bar_graph linked_question: Q7 description: Vertical bar graph showing museum visitors from Monday to Friday labels: Days: Mon, Tue, Wed, Thu, Fri; Y-axis: Number of visitors (scale 0-500, intervals of 50) values: Mon: 120, Tue: 180, Wed: 250, Thu: 200, Fri: 300 must_show: All 5 bars with correct heights, labelled axes, title "Museum Visitors (Mon-Fri)" </image_placeholder>

(a) On which day did the museum have the most visitors?
Answer: _______ [1]

(b) How many more visitors were there on Friday than on Monday?
Answer: _______ [1]

8. The pie chart shows how John spent his monthly allowance of $240.

<image_placeholder> id: Q8-fig1 type: pie_chart linked_question: Q8 description: Pie chart showing John's monthly allowance spending labels: Food (120°), Transport (60°), Savings (90°), Entertainment (90°) values: Total allowance = $240 must_show: Four sectors with correct angles, legend, title "John's Monthly Allowance Spending" </image_placeholder>

(a) What fraction of his allowance did John spend on food? Give your answer in simplest form.
Answer: _______ [1]

(b) How much money did John save?
Answer: $_______ [1]

9. The line graph shows the height of a plant measured at the end of each week for 6 weeks.

<image_placeholder> id: Q9-fig1 type: line_graph linked_question: Q9 description: Line graph showing plant height over 6 weeks labels: X-axis: Week (1, 2, 3, 4, 5, 6); Y-axis: Height (cm) from 0 to 30 values: Week 1: 5cm, Week 2: 9cm, Week 3: 14cm, Week 4: 18cm, Week 5: 21cm, Week 6: 23cm must_show: Points plotted and connected, labelled axes, title "Plant Height Over 6 Weeks" </image_placeholder>

(a) What was the height of the plant at the end of Week 3?
Answer: _______ cm [1]

(b) Between which two consecutive weeks did the plant grow the most?
Answer: Week _______ to Week _______ [1]

10. The table shows the scores of 20 students in a Mathematics quiz.

Score	1	2	3	4	5
Frequency	2	4	6	5	3

(a) Find the median score.
Answer: _______ [1]

(b) Find the mean score. Give your answer correct to 1 decimal place.
Answer: _______ [1]

11. The average mass of 4 boxes is 12.5 kg. When a fifth box is added, the average mass becomes 13.2 kg. What is the mass of the fifth box?

Answer: _______ kg [3]

12. The bar graph shows the number of cars sold by a dealer in the first 6 months of the year.

<image_placeholder> id: Q12-fig1 type: bar_graph linked_question: Q12 description: Vertical bar graph showing cars sold per month for 6 months labels: Months: Jan, Feb, Mar, Apr, May, Jun; Y-axis: Cars sold (scale 0-60, intervals of 10) values: Jan: 25, Feb: 30, Mar: 40, Apr: 35, May: 45, Jun: 50 must_show: All 6 bars with correct heights, labelled axes, title "Cars Sold (Jan-Jun)" </image_placeholder>

(a) In which month was the increase in cars sold the greatest compared to the previous month?
Answer: _______ [1]

(b) What percentage of the total cars sold in the 6 months were sold in June? Give your answer correct to 1 decimal place.
Answer: _______% [2]

13. The pie chart shows the types of pets owned by 180 families.

<image_placeholder> id: Q13-fig1 type: pie_chart linked_question: Q13 description: Pie chart showing pet ownership of 180 families labels: Dogs (100°), Cats (80°), Birds (60°), Fish (70°), Others (50°) values: Total families = 180 must_show: Five sectors with correct angles, legend, title "Types of Pets Owned by 180 Families" </image_placeholder>

(a) How many families own dogs?
Answer: _______ [1]

(b) How many more families own cats than birds?
Answer: _______ [1]

14. The table shows the number of hours 15 students spent on homework in a week.

Hours	2	3	4	5	6	7
Frequency	1	2	4	3	3	2

(a) What is the mode of the number of hours?
Answer: _______ [1]

(b) Find the median number of hours.
Answer: _______ [1]

15. The line graph shows the amount of water in a tank over 8 hours.

<image_placeholder> id: Q15-fig1 type: line_graph linked_question: Q15 description: Line graph showing water volume in tank over 8 hours labels: X-axis: Time (hours) 0, 1, 2, 3, 4, 5, 6, 7, 8; Y-axis: Volume (litres) 0 to 500 values: 0h: 500L, 1h: 450L, 2h: 400L, 3h: 350L, 4h: 300L, 5h: 250L, 6h: 200L, 7h: 150L, 8h: 100L must_show: Points plotted and connected with straight line, labelled axes, title "Water Volume in Tank Over 8 Hours" </image_placeholder>

(a) At what rate (in litres per hour) is the water decreasing?
Answer: _______ L/h [1]

(b) How much water was in the tank at the start?
Answer: _______ L [1]

Section C: Long Answer Questions (Questions 16–20, 4 marks each)

16. The table below shows the number of stamps collected by 5 children.

Child	Ali	Ben	Cindy	Devi	Eli
Stamps	45	60	35	55	25

(a) Find the average number of stamps collected by the 5 children.
Answer: _______ [1]

(b) Ali gave some stamps to Eli so that they both had the same number of stamps. How many stamps did Ali give to Eli?
Answer: _______ [2]

17. A survey was conducted on the favourite sports of 300 students. The results are shown in the pie chart.

<image_placeholder> id: Q17-fig1 type: pie_chart linked_question: Q17 description: Pie chart showing favourite sports of 300 students labels: Swimming (72°), Badminton (90°), Football (108°), Basketball (54°), Others (36°) values: Total students = 300 must_show: Five sectors with correct angles, legend, title "Favourite Sports of 300 Students" </image_placeholder>

(a) How many students chose swimming as their favourite sport?
Answer: _______ [1]

(b) What percentage of students chose basketball?
Answer: _______% [1]

(c) The number of students who chose football is twice the number who chose basketball. Verify if this statement is correct.
Answer: _______ [1]

(d) If 20 students who chose "Others" changed their choice to badminton, what would be the new angle for badminton in the pie chart?
Answer: _______° [1]

18. The bar graph shows the number of books sold by a bookshop from Monday to Sunday.

<image_placeholder> id: Q18-fig1 type: bar_graph linked_question: Q18 description: Vertical bar graph showing books sold each day of the week labels: Days: Mon, Tue, Wed, Thu, Fri, Sat, Sun; Y-axis: Books sold (scale 0-140, intervals of 20) values: Mon: 40, Tue: 50, Wed: 60, Thu: 55, Fri: 70, Sat: 120, Sun: 100 must_show: All 7 bars with correct heights, labelled axes, title "Books Sold in a Week" </image_placeholder>

(a) What is the total number of books sold in the week?
Answer: _______ [1]

(b) Find the average number of books sold per day.
Answer: _______ [1]

(d) The bookshop owner claims that weekend sales (Sat and Sun) make up more than half of the weekly sales. Is he correct? Explain your answer.
Answer: _______ [1]

19. The table shows the marks obtained by 25 students in a Science test.

Marks	40-49	50-59	60-69	70-79	80-89	90-99
Frequency	2	3	5	7	6	2

(a) How many students scored 70 marks and above?
Answer: _______ [1]

(b) In which class interval does the median lie?
Answer: _______ [1]

(c) Estimate the mean mark using the midpoint of each class interval. Give your answer correct to 1 decimal place.
Answer: _______ [2]

20. The line graph shows the distance travelled by a cyclist over 5 hours.

<image_placeholder> id: Q20-fig1 type: line_graph linked_question: Q20 description: Line graph showing distance travelled by cyclist over 5 hours labels: X-axis: Time (hours) 0, 1, 2, 3, 4, 5; Y-axis: Distance (km) 0 to 60 values: 0h: 0km, 1h: 12km, 2h: 24km, 3h: 33km, 4h: 40km, 5h: 45km must_show: Points plotted and connected, labelled axes, title "Distance Travelled by Cyclist" </image_placeholder>

(a) What was the cyclist's speed in the first hour?
Answer: _______ km/h [1]

(b) During which hour was the cyclist's speed the slowest?
Answer: _______ [1]

(d) The cyclist took a 30-minute break during the journey. During which hour did the break most likely occur? Explain your reasoning.
Answer: _______ [1]

End of Quiz

Answers

Primary 6 PSLE Mathematics Quiz - Data Analysis (Answer Key)

Total Marks: 50

Section A: Multiple Choice Questions (Questions 1–5, 2 marks each)

1. Answer: B. 18 [2]

Working:

Total books = 15 + 22 + 18 + 25 + 10 = 90
Number of students = 5
Average = 90 ÷ 5 = 18

Key concept: Average = Sum of values ÷ Number of values

2. Answer: C. 60 [2]

Working:

Angle for bananas = 108°
Total angle in pie chart = 360°
Fraction for bananas = 108°/360° = 3/10
Number of students = 3/10 × 200 = 60

Key concept: In a pie chart, angle of sector ÷ 360° = fraction of total

3. Answer: C. 1 and 3 [2]

Working:

Frequency of 1 goal = 3
Frequency of 2 goals = 2
Frequency of 3 goals = 3
Frequency of 4 goals = 1
Highest frequency = 3 (occurs for both 1 goal and 3 goals)
Mode = 1 and 3 (bimodal)

Key concept: Mode is the value(s) with the highest frequency. There can be more than one mode.

4. Answer: B. 9am to 12pm [2]

Working:

6am to 9am: 26°C - 22°C = 4°C increase
9am to 12pm: 32°C - 26°C = 6°C increase
12pm to 3pm: 34°C - 32°C = 2°C increase
3pm to 6pm: 30°C - 34°C = -4°C (decrease)
Greatest increase = 6°C (9am to 12pm)

Key concept: Read values from line graph, calculate differences between consecutive points.

5. Answer: C. 34 [2]

Working:

Sum of 6 numbers = 6 × 24 = 144
Sum of remaining 5 numbers = 5 × 22 = 110
Number removed = 144 - 110 = 34

Key concept: When average changes after removing a value, find the difference in totals.

Section B: Short Answer Questions (Questions 6–15, 3 marks each)

6. (a) Answer: 25 [1]

Working: 4 + 8 + 6 + 5 + 2 = 25 pupils

(b) Answer: 55 [1]

Working: (0×4) + (1×8) + (2×6) + (3×5) + (4×2) = 0 + 8 + 12 + 15 + 8 = 43 books

Working: Average = 43 ÷ 25 = 1.72 ≈ 1.7 (1 decimal place)

Marking notes: 1 mark each part. For (c), accept 1.7 or 1.72 if not rounded.

7. (a) Answer: Friday [1]

(b) Answer: 180 [1]

Working: 300 - 120 = 180

Working: (120 + 180 + 250 + 200 + 300) ÷ 5 = 1050 ÷ 5 = 210

8. (a) Answer: 1/3 [1]

Working: 120°/360° = 1/3

(b) Answer: $60 [1]

Working: 90°/360° × $240 = 1/4 ×$ 240 = $60

Working: 90°/360° × 100% = 25%

Key concept: Fraction = Angle/360°, Amount = Fraction × Total, Percentage = Fraction × 100%

9. (a) Answer: 14 [1]

(b) Answer: Week 2 to Week 3 [1]

Working:

Week 1 to 2: 9 - 5 = 4 cm
Week 2 to 3: 14 - 9 = 5 cm (greatest)
Week 3 to 4: 18 - 14 = 4 cm
Week 4 to 5: 21 - 18 = 3 cm
Week 5 to 6: 23 - 21 = 2 cm

Working: Total growth = 23 - 5 = 18 cm over 5 intervals (or 6 weeks from start) Average per week = 18 ÷ 6 = 3 cm/week

Note: Average growth per week = (Final height - Initial height) ÷ Number of weeks

10. (a) Answer: 3 [1]

Working: 20 students, median is average of 10th and 11th values. Cumulative frequency: 2 (score 1), 6 (score 2), 12 (score 3) → 10th and 11th are both 3.

(b) Answer: 3.2 [1]

Working: Mean = (1×2 + 2×4 + 3×6 + 4×5 + 5×3) ÷ 20 = (2 + 8 + 18 + 20 + 15) ÷ 20 = 63 ÷ 20 = 3.15 ≈ 3.2

Working: Range = Highest - Lowest = 5 - 1 = 4

11. Answer: 16 kg [3]

Working:

Total mass of 4 boxes = 4 × 12.5 = 50 kg
Total mass of 5 boxes = 5 × 13.2 = 66 kg
Mass of 5th box = 66 - 50 = 16 kg

Mark breakdown:

1 mark: Total mass of 4 boxes = 50 kg
1 mark: Total mass of 5 boxes = 66 kg
1 mark: Correct answer 16 kg

12. (a) Answer: March [1]

Working:

Jan to Feb: 30 - 25 = 5
Feb to Mar: 40 - 30 = 10 (greatest)
Mar to Apr: 35 - 40 = -5
Apr to May: 45 - 35 = 10
May to Jun: 50 - 45 = 5
Greatest increase = 10 (Feb to Mar and Apr to May). Accept March or May.

Note: Both March and May show increase of 10. Accept either with correct working.

(b) Answer: 22.7% [2]

Working:

Total cars = 25 + 30 + 40 + 35 + 45 + 50 = 225
June cars = 50
Percentage = 50/225 × 100% = 22.222...% ≈ 22.2% (1 d.p.)

Mark breakdown:

1 mark: Correct total (225)
1 mark: Correct percentage calculation and rounding

13. (a) Answer: 50 [1]

Working: 100°/360° × 180 = 50 families

(b) Answer: 10 [1]

Working:

Cats: 80°/360° × 180 = 40 families
Birds: 60°/360° × 180 = 30 families
Difference = 40 - 30 = 10

Working: 70°/360° = 7/36 (simplest form)

14. (a) Answer: 4 [1]

Working: Highest frequency = 4 (for 4 hours)

(b) Answer: 4.5 [1]

Working: 15 students, median is 8th value. Cumulative: 1 (2h), 3 (3h), 7 (4h), 10 (5h) → 8th value is 5 hours? Wait, let me recount. 1 student at 2h, 2 at 3h (cum 3), 4 at 4h (cum 7), 3 at 5h (cum 10), 3 at 6h (cum 13), 2 at 7h (cum 15). 8th value falls in 5 hours group. So median = 5.

Correction: Median = 5 hours [1]

Working: Mean = (2×1 + 3×2 + 4×4 + 5×3 + 6×3 + 7×2) ÷ 15 = (2 + 6 + 16 + 15 + 18 + 14) ÷ 15 = 71 ÷ 15 = 4.733... ≈ 4.7

15. (a) Answer: 50 [1]

Working: Decrease per hour = (500 - 450) = 50 L/h (constant rate)

(b) Answer: 500 [1]

Working: At 0 hours, volume = 500 L

Working: 500 L ÷ 50 L/h = 10 hours

Section C: Long Answer Questions (Questions 16–20, 4 marks each)

16. (a) Answer: 44 [1]

Working: (45 + 60 + 35 + 55 + 25) ÷ 5 = 220 ÷ 5 = 44

(b) Answer: 10 [2]

Working:

Ali has 45, Eli has 25. Total = 70.
For equal amounts, each should have 70 ÷ 2 = 35.
Ali gives 45 - 35 = 10 stamps to Eli.

Mark breakdown:

1 mark: Correct total (70) or target each (35)
1 mark: Correct answer 10

Working: Total stamps unchanged (220), number of children unchanged (5). Average remains 44.

Key concept: Transferring between members doesn't change the total or average.

17. (a) Answer: 60 [1]

Working: 72°/360° × 300 = 60 students

(b) Answer: 15% [1]

Working: 54°/360° × 100% = 15%

Working:

Football: 108°/360° × 300 = 90 students
Basketball: 54°/360° × 300 = 45 students
90 = 2 × 45, so statement is correct.

(d) Answer: 108° [1]

Working:

Original badminton: 90° (75 students)
Others: 36° (30 students)
20 students move from Others to Badminton
New badminton = 75 + 20 = 95 students
New angle = 95/300 × 360° = 114°

Correction: Let me recalculate. Original badminton students = 90/360 × 300 = 75 Original others = 36/360 × 300 = 30 After change: Badminton = 75 + 20 = 95, Others = 30 - 20 = 10 New badminton angle = 95/300 × 360° = 114°

Answer: 114° [1]

18. (a) Answer: 495 [1]

Working: 40 + 50 + 60 + 55 + 70 + 120 + 100 = 495

(b) Answer: 70.7 [1]

Working: 495 ÷ 7 = 70.714... ≈ 70.7 (or 70 5/7)

Working: Average ≈ 70.7. Days above: Fri (70? No, 70 < 70.7), Sat (120), Sun (100). Only 2 days? Wait. Mon 40, Tue 50, Wed 60, Thu 55, Fri 70, Sat 120, Sun 100. Average = 70.7. Above average: Sat (120), Sun (100). That's 2 days. But Fri = 70 which is below 70.7. So answer = 2.

Correction: Answer: 2 [1]

(d) Answer: Yes, he is correct. [1]

Working: Weekend sales = 120 + 100 = 220. Total = 495. Half = 247.5. 220 < 247.5, so weekend sales are LESS than half. The owner is NOT correct.

Correction: Answer: No, he is not correct. Weekend sales (220) is less than half of 495 (247.5). [1]

19. (a) Answer: 15 [1]

Working: 70-79: 7, 80-89: 6, 90-99: 2. Total = 7 + 6 + 2 = 15

(b) Answer: 70-79 [1]

Working: 25 students, median is 13th value. Cumulative: 2 (40-49), 5 (50-59), 10 (60-69), 17 (70-79). 13th falls in 70-79.

Working:

Marks	Midpoint (x)	Freq (f)	f×x
40-49	44.5	2	89
50-59	54.5	3	163.5
60-69	64.5	5	322.5
70-79	74.5	7	521.5
80-89	84.5	6	507
90-99	94.5	2	189
Total		25	1792.5

Mean = 1792.5 ÷ 25 = 71.7

Correction: Let me recalculate midpoints and products. 44.5×2 = 89 54.5×3 = 163.5 64.5×5 = 322.5 74.5×7 = 521.5 84.5×6 = 507 94.5×2 = 189 Sum = 89 + 163.5 + 322.5 + 521.5 + 507 + 189 = 1792.5 Mean = 1792.5/25 = 71.7

Answer: 71.7 [2]

Mark breakdown:

1 mark: Correct midpoints and f×x calculations
1 mark: Correct mean 71.7

20. (a) Answer: 12 [1]

Working: Distance in 1st hour = 12 - 0 = 12 km. Speed = 12 km/h.

(b) Answer: 5th hour (4h to 5h) [1]

Working:

1st hour: 12 km/h
2nd hour: 24 - 12 = 12 km/h
3rd hour: 33 - 24 = 9 km/h
4th hour: 40 - 33 = 7 km/h
5th hour: 45 - 40 = 5 km/h (slowest)

Working: Total distance = 45 km, Total time = 5 h. Average speed = 45 ÷ 5 = 9 km/h.

(d) Answer: 4th hour (3h to 4h) or 5th hour (4h to 5h) [1]

Working: The speed decreases gradually (12, 12, 9, 7, 5 km/h). A break would show zero distance covered. Since distance increases every hour (no flat segment), the break is not clearly visible. However, the lowest speed is in the 5th hour (5 km/h), suggesting fatigue or a break near the end. Most likely the break occurred during the 4th to 5th hour when speed dropped to 5 km/h.

Acceptable reasoning: The cyclist's speed decreased each hour after the 2nd hour. The sharpest drop is from 7 km/h to 5 km/h (4th to 5th hour), suggesting a break during the 5th hour. Or: No clear break visible as distance increases continuously; the decreasing speed suggests fatigue rather than a break.

Marking note: Accept reasonable explanation with reference to graph data.

End of Answer Key