O Level Elementary Mathematics Statistics Probability Quiz

O-Level Elementary Mathematics Quiz - Statistics Probability (Answer Key)

Total Marks: 40
Topic: Statistics & Probability

Section A: Data Handling and Statistics (Q1–8)

Q1 [2 marks]
Total books = (0×4) + (1×9) + (2×8) + (3×6) + (4×3)
= 0 + 9 + 16 + 18 + 12 = 55
Answer: 55 books
Teaching note: Multiply each book count by its frequency then sum. Common mistake: adding frequencies only (30) instead of weighted total.

Q2 [2 marks]
Mean = total books ÷ number of students = 55 ÷ 30 = 1.833...
Correct to 2 dp: 1.83
Teaching note: Mean = sum of values ÷ number of data points. Show division and rounding.

Q3 [1 mark]
Ordered masses: 4.8, 4.9, 5, 5, 5, 5.1, 5.2
Middle (4th) value = 5
Answer: 5 kg
Teaching note: Median is the middle value of ordered data. For 7 values, the 4th is median.

Q4 [1 mark]
12 appears 3 times (most frequent).
Answer: 12
Teaching note: Mode is the most frequently occurring value.

Q5 [1 mark]
Range = max − min = 15 − 3 = 12
Answer: 12
Teaching note: Range shows spread; subtract smallest from largest.

Q6 [2 marks]
Total angle = 360°. Given: Bus 90° + MRT 120° + Walk 90° = 300°.
Cycle angle = 360° − 300° = 60°.
Number = (60/360) × 120 = 20
Answer: 20 students
Teaching note: Pie angle proportional to frequency. Fraction of circle × total.

Q7 [1 mark]
Highest frequency is 8 at mark 30.
Answer: 30
Teaching note: Modal class/mark from frequency table.

Q8 [2 marks]
Total marbles = 5+3+2 = 10. Blue = 3.
P(blue) = 3/10 (already simplest).
Answer: 3/10
Teaching note: Probability = favourable ÷ total outcomes.

Section B: Probability (Q9–14)

Q9 [1 mark]
Possible outcomes: HH, HT, TH, TT
Answer: HH, HT, TH, TT
Teaching note: Two coins, each H or T; 2² = 4 outcomes.

Q10 [2 marks]
Exactly one head: HT, TH → 2 outcomes.
P = 2/4 = 1/2
Answer: 1/2
Teaching note: Count favourable over total. Simplify fraction.

Q11 [2 marks]
Total = 10. Not black = white = 4.
P(not black) = 4/10 = 2/5
Answer: 2/5
Teaching note: Complement approach: 1 − P(black) also works.

Q12 [1 mark]
Even: 2,4 → 2 outcomes of 4.
P = 2/4 = 1/2
Answer: 1/2
Teaching note: Equal sectors → equally likely.

Q13 [2 marks]
Shaded is in A but not in B → A ∩ B'
Answer: A ∩ B'
Teaching note: Complement B' means outside B. Intersection with A gives left crescent. Common trap: writing A ∪ B'.

Q14 [2 marks]
Queens = 4 (one per suit). Total = 52.
P(queen) = 4/52 = 1/13
Answer: 1/13
Teaching note: Standard pack has 4 queens.

Section C: Interpretation and Combined (Q15–20)

Q15 [2 marks]
Total visitors = 40+55+50+70+65 = 280.
Mean = 280 ÷ 5 = 56
Answer: 56
Teaching note: From line graph read values; sum and divide by 5 days.

Q16 [1 mark]
Highest point = Thu (70).
Answer: Thursday
Teaching note: Read max from graph.

Q17 [2 marks]
Like football only = 14−5 = 9; badminton only = 11−5 = 6; both = 5.
Total liking at least one = 9+6+5 = 20.
Neither = 25 − 20 = 5
Answer: 5 students
Teaching note: Venn: subtract overlap before adding. Universal − union.

Q18 [1 mark]

4 means 5,6 → 2 of 6.
P = 2/6 = 1/3
Answer: 1/3
Teaching note: Die has 6 faces.

Q19 [3 marks]
Cumulative: 5(1), 6(2→3), 7(4→7), 8(2→9), 9(1→10).
10 data points → median = average of 5th & 6th.
Ordered: 5,6,6,7,7,7,7,8,8,9. 5th=7, 6th=7.
Median = (7+7)/2 = 7
Answer: 7 [1 for ordering, 2 for correct median calc]
Teaching note: Even count → mean of middle two.

Q20 [3 marks]
Word: P R O B A B I L I T Y → 11 letters.
B appears at positions 4 and 6 → 2 B's.
P(B) = 2/11
Answer: 2/11 [1 for count letters, 1 for count B, 1 for fraction]
Teaching note: Distinguish letters; probability = favourable/total.