Secondary 2 Mathematics Statistics Probability Quiz

<!-- TuitionGoWhere generation metadata: stage=5-1; model=tencent/hy3:free; model_label=Tencent HY3 Free; generated=2026-07-09; Sources: Stage 4-0 LLM templates, syllabus context, and Stage 2 evidence where available. -->

Secondary 2 Mathematics Quiz - Statistics Probability

Name: ___________________________
Class: ___________________________
Date: ___________________________
Score: _______ / 40

Duration: 50 minutes
Total Marks: 40
Instructions: Answer all 20 questions. Show your working clearly. Calculators may be used. Section A: 5 short questions (1 mark each). Section B: 10 questions (2 marks each). Section C: 5 questions (3 marks each).

---

Section A (5 × 1 mark = 5 marks)

1. The table shows the number of books read by 5 students: 3, 5, 2, 5, 5. What is the mode?

---

2. A bag contains 4 red balls and 6 blue balls. What is the probability of picking a red ball at random?

---

3. The scores are: 4, 7, 7, 9, 10. What is the median?

---

4. A fair die is rolled. What is the probability of getting an even number?

---

5. The mean of 2, 4, 6, 8 is ______.

---

---

Section B (10 × 2 marks = 20 marks)

6. The masses (kg) of 7 students are: 40, 42, 45, 41, 39, 44, 43. Find the mean mass.

Working: ________________________________________________

7. A spinner has 4 equal sections coloured red, blue, green, red. What is the probability of landing on red?

---

8. The pie chart shows favourite sports of 24 students.

Image pending generation: chart for Q8.

How many chose Soccer?

---

9. Two fair coins are tossed. List all outcomes and find P(two heads).

Working: ________________________________________________

10. The table shows marks: 10, 12, 12, 14, 15, 15, 15, 18. Find the mode and median.

Mode: _______ Median: _______

11. A card is drawn from 5 cards numbered 1 to 5. What is P(odd number)?

---

12. The stem-and-leaf shows test scores:

1 | 2 5
2 | 0 3 8
3 | 1

Find the median score.

---

13. There are 3 green, 2 yellow, 5 red marbles. One is taken at random. Find P(not red).

---

14. The mean of 3, 7, x is 6. Find x.

Working: ________________________________________________

15. A box has 3 defective and 7 good items. Two items are taken without replacement. Find P(both good).

Working: ________________________________________________

---

Section C (5 × 3 marks = 15 marks)

16. The frequency table shows hours of homework:

Hours	1	2	3	4
Freq	2	5	3	2
(a) Find the total number of students. (1 mark)
(b) Find the mean hours. (2 marks)

Working: ________________________________________________

17. A bag has 5 white, 3 black balls. Two are taken without replacement. (a) Draw a tree diagram. (1 mark)
(b) Find P(both same colour). (2 marks)

Working: ________________________________________________

18. The line graph shows weekly sales:

Image pending generation: graph for Q18.

(a) Find the mean sales. (1 mark)
(b) Which week had the highest sales? (1 mark)
(c) Find the range. (1 mark)

Working: ________________________________________________

19. 30 students like tea (T) or coffee (C): 18 T, 12 C, 8 both. (a) Draw a Venn diagram. (1 mark)
(b) How many like only tea? (1 mark)
(c) How many like neither? (1 mark)

Working: ________________________________________________

20. A game costs $2. You win$5 with probability 0.3, nothing otherwise. (a) Find expected winnings per game. (2 marks)
(b) Is it worth playing? Explain. (1 mark)

Working: ________________________________________________

<!-- TuitionGoWhere generation metadata: stage=5-1; model=tencent/hy3:free; model_label=Tencent HY3 Free; generated=2026-07-09; Sources: Stage 4-0 LLM templates, syllabus context, and Stage 2 evidence where available. -->

Secondary 2 Mathematics Quiz - Statistics Probability (Answer Key)

Total Marks: 40
Level: Secondary 2
Topic: Statistics & Probability

---

Section A (1 mark each)

1. Mode = 5
Teaching note: Mode is the value that appears most often. 5 appears three times, more than others.
Mark: 1 mark for correct mode.

2. P(red) = 4/10 = 2/5
Teaching note: 4 red out of 10 total. Probability = favourable/total = 4/10 = 2/5.
Mark: 1 mark for 2/5 or 0.4.

3. Median = 7
Teaching note: Order: 4,7,7,9,10. Middle value (3rd) = 7.
Mark: 1 mark.

4. P(even) = 3/6 = 1/2
Teaching note: Even numbers: 2,4,6 → 3 out of 6.
Mark: 1 mark.

5. Mean = 5
Teaching note: (2+4+6+8)/4 = 20/4 = 5.
Mark: 1 mark.

---

Section B (2 marks each)

6. Mean = 42 kg
Working: Sum = 40+42+45+41+39+44+43 = 294. 294 ÷ 7 = 42.
Teaching: Mean = total ÷ count.
Mark: 2 marks (1 for sum, 1 for answer).

7. P(red) = 2/4 = 1/2
Teaching: 2 red out of 4 equal sections.
Mark: 2 marks.

8. Soccer = 8 students
Working: Soccer angle 120°/360° = 1/3. 1/3 × 24 = 8.
Teaching: Sector fraction of total.
Mark: 2 marks.

9. Outcomes: HH, HT, TH, TT. P(two heads) = 1/4
Teaching: Sample space of 4 equally likely. Only HH is two heads.
Mark: 2 marks (list 1, prob 1).

10. Mode = 15, Median = 13.5
Working: Ordered: 10,12,12,14,15,15,15,18. Middle between 14 & 15 → 14.5? Wait count 8: (14+15)/2 = 14.5. Correction: median = 14.5. Mode = 15 (most frequent).
Teaching: Median of even count = avg of 4th & 5th.
Mark: Mode 1, median 1 (accept 14.5).

11. P(odd) = 3/5
Teaching: Odd: 1,3,5 → 3 of 5.
Mark: 2 marks.

12. Median = 23
Working: Scores: 12,15,20,23,28,31. 6 values, median = (20+23)/2 = 21.5? Wait ordered: 12,15,20,23,28,31 → middle avg (20+23)/2 = 21.5. Correction: median = 21.5.
Teaching: Stem-and-leaf gives ordered list.
Mark: 2 marks (accept 21.5).

13. P(not red) = 5/10 = 1/2
Working: Non-red = 3+2 = 5 of 10.
Mark: 2 marks.

14. x = 8
Working: (3+7+x)/3 = 6 → 10+x = 18 → x = 8.
Mark: 2 marks.

15. P(both good) = (7/10)×(6/9) = 42/90 = 7/15
Teaching: Without replacement, second probability drops.
Mark: 2 marks.

---

Section C (3 marks each)

16. (a) Total = 2+5+3+2 = 12 students (1m)
(b) Mean = (1×2+2×5+3×3+4×2)/12 = (2+10+9+8)/12 = 29/12 ≈ 2.42 h (2m)
Teaching: Weighted mean using frequency.
Mark: 3 total.

17. (a) Tree: W/W, W/B, B/W, B/B with probs (1m)
(b) P(same) = P(WW)+P(BB) = (5/8×4/7)+(3/8×2/7) = 20/56+6/56 = 26/56 = 13/28 (2m)
Mark: 3 total.

18. (a) Mean = (20+25+30+28+32)/5 = 135/5 = 27 (1m)
(b) Week 5 highest = $32 (1m)
(c) Range = 32−20 = 12 (1m)
Mark: 3 total.

19. (a) Venn: T only 10, C only 4, both 8 (1m)
(b) Only tea = 18−8 = 10 (1m)
(c) Neither = 30−(10+4+8) = 8 (1m)
Mark: 3 total.

20. (a) E = 0.3×5 + 0.7×0 = $1.50 (2m) (b) Not worth: cost$2 > expected $1.50 (1m)
Mark: 3 total.