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O Level Elementary Mathematics Statistics Probability Quiz

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O Level Elementary Mathematics AI Generated Generated by Qwen3.6 Plus Updated 2026-08-17

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Questions

O-Level Elementary Mathematics Quiz - Statistics Probability

Name: __________________________
Class: __________________________
Date: __________________________
Score: ________ / 50

Duration: 60 minutes
Total Marks: 50

Instructions:

Answer all questions.
Write your answers in the spaces provided.
Show all necessary working clearly; no marks will be given for correct answers without working.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless otherwise specified.
An approved calculator is allowed.

Section A: Data Representation and Measures of Central Tendency (15 marks)

1. The heights, $h$ cm, of 10 students are recorded as follows: $152, 158, 160, 160, 165, 168, 170, 172, 175, 180$

(a) Find the mode.
[1]

(b) Find the median.
[1]

Answer space

2. The table below shows the number of goals scored by a football team in 20 matches.

Number of Goals	0	1	2	3	4
Frequency	3	6	5	4	2

(a) Calculate the mean number of goals scored per match.
[2]

(b) State the modal number of goals.
[1]

Answer space

3. A stem-and-leaf diagram shows the ages of participants in a marathon. Key: $2 | 5$ represents 25 years.

2 | 1 3 5 5 8
3 | 0 2 4 4 6 9
4 | 1 1 3 7
5 | 0 2

(a) How many participants are there?
[1]

(b) Find the range of the ages.
[1]

Answer space

4. The mean of five numbers is 12. Four of the numbers are 8, 10, 14, and 15. Find the fifth number.
[2]

Answer space

5. The table shows the distribution of marks obtained by 40 students in a test.

Mark ( $x$ )	1	2	3	4	5
Frequency ( $f$ )	4	8	12	10	6

Calculate the mean mark.
[3]

Answer space

Section B: Cumulative Frequency and Box-and-Whisker Plots (15 marks)

6. The cumulative frequency table below shows the time taken, $t$ minutes, by 50 students to complete a puzzle.

Time ( $t$ min)	$t \le 10$	$t \le 20$	$t \le 30$	$t \le 40$	$t \le 50$
Cumulative Frequency	5	15	32	45	50

(a) Draw a cumulative frequency curve for this information on the grid below.
[3]

(Note: In a real exam, a grid would be provided. For this quiz, sketch the shape or describe the coordinates plotted.)

(b) Use your curve to estimate: (i) the median time,
[1]

(ii) the interquartile range.
[2]

Answer space

7. The box-and-whisker plot below summarizes the test scores of Class A.

Minimum: 20
Lower Quartile ( $Q_1$ ): 45
Median: 60
Upper Quartile ( $Q_3$ ): 75
Maximum: 95

(a) Calculate the interquartile range for Class A.
[1]

(b) Class B has a median score of 65 and an interquartile range of 20. (i) Which class has the higher median score?
[1]

(ii) Which class has more consistent scores? Explain your answer.
[2]

Answer space

8. The heights of 100 plants are measured. The cumulative frequency curve is used to find the quartiles.

$Q_1 = 12$ cm
Median = 18 cm
$Q_3 = 25$ cm

(a) How many plants have a height less than 12 cm?
[1]

(b) How many plants have a height between 12 cm and 25 cm?
[1]

Answer space

9. A dataset has a lower quartile of 30 and an upper quartile of 50. (a) Calculate the interquartile range.
[1]

(b) An outlier is defined as any value greater than $Q_3 + 1.5 \times \text{IQR}$ . Determine the threshold value above which a data point is considered an outlier.
[2]

Answer space

10. Two groups of students took the same quiz.

Group X: Median = 70, IQR = 10
Group Y: Median = 70, IQR = 25

Explain what the difference in IQR tells you about the performance of the two groups.
[2]

Answer space

Section C: Probability (20 marks)

11. A fair six-sided die is thrown once. (a) Find the probability of getting a number greater than 4.
[1]

(b) Find the probability of getting an even number.
[1]

Answer space

12. A bag contains 5 red balls, 3 blue balls, and 2 green balls. A ball is chosen at random. (a) Find the probability that the ball is red.
[1]

(b) Find the probability that the ball is not blue.
[1]

Answer space

13. Two fair coins are tossed. (a) List all the possible outcomes in the sample space.
[1]

(b) Find the probability of getting exactly one head.
[1]

Answer space

14. A spinner has 8 equal sections numbered 1 to 8. (a) Find the probability of spinning a prime number.
[2]

(b) Find the probability of spinning a number that is a multiple of 3.
[1]

Answer space

15. A bag contains 4 white balls and 6 black balls. Two balls are drawn from the bag without replacement. (a) Draw a tree diagram to represent the possible outcomes.
[2]

(b) Find the probability that both balls are white.
[2]

Answer space

16. The probability that it rains on any given day in April is 0.3. (a) Find the probability that it does not rain on a given day.
[1]

(b) Find the probability that it rains on two consecutive days. Assume the events are independent.
[2]

Answer space

17. In a class of 30 students, 18 study Mathematics, 15 study Physics, and 5 study neither. (a) Draw a Venn diagram to illustrate this information.
[2]

(b) Find the probability that a student chosen at random studies both Mathematics and Physics.
[2]

Answer space

18. A box contains 10 cards numbered 1 to 10. One card is drawn at random. Let $A$ be the event that the number is even. Let $B$ be the event that the number is greater than 6.

(a) Find $P(A)$ .
[1]

(b) Find $P(A \cap B)$ .
[1]

Answer space

19. A biased coin is thrown. The probability of getting a Head is 0.6. The coin is thrown three times. Find the probability of getting: (a) Three Heads.
[1]

(b) At least one Tail.
[2]

Answer space

20. The table shows the probabilities of outcomes for a spinner with three colors: Red, Blue, and Green.

Color	Red	Blue	Green
Probability	0.5	0.3	$p$

(a) Find the value of $p$ .
[1]

(b) The spinner is spun twice. Find the probability that it lands on Green both times.
[2]

Answer space

*** End of Quiz ***

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Answers

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

1. (a) Mode = 160 (appears twice) [1] (b) Median = $\frac{165 + 168}{2} =$ 166.5 [1] (c) Mean = $\frac{152+158+160+160+165+168+170+172+175+180}{10} = \frac{1660}{10} =$ 166 [2]

2. (a) Mean = $\frac{(0\times3) + (1\times6) + (2\times5) + (3\times4) + (4\times2)}{20} = \frac{0+6+10+12+8}{20} = \frac{36}{20} =$ 1.8 [2] (b) Mode = 1 (highest frequency) [1]

3. (a) Total participants = $5 + 6 + 4 + 2 =$ 17 [1] (b) Range = $52 - 21 =$ 31 [1] (c) Median is the 9th value. Values: 21, 23, 25, 25, 28, 30, 32, 34, 34, 36... Median = 34 [1]

4. Sum of 5 numbers = $5 \times 12 = 60$ . Sum of 4 numbers = $8 + 10 + 14 + 15 = 47$ . Fifth number = $60 - 47 =$ 13 [2]

5. Mean = $\frac{(1\times4) + (2\times8) + (3\times12) + (4\times10) + (5\times6)}{40}$ $= \frac{4 + 16 + 36 + 40 + 30}{40} = \frac{126}{40} =$ 3.15 [3]

6. (a) Plot points: $(10,5), (20,15), (30,32), (40,45), (50,50)$ . Join with smooth curve. [3] (b) (i) Median (50% of 50 = 25th value). From curve/graph interpolation: Between 20 and 30. Linear interpolation: $\frac{25-15}{32-15} \times 10 + 20 \approx 25.9$ . Accept 26 min. [1] (ii) $Q_1$ (12.5th value) $\approx 23.5$ . $Q_3$ (37.5th value) $\approx 36.5$ . IQR = $36.5 - 23.5 =$ 13 min. (Accept range 12-14 based on drawing). [2]

7. (a) IQR = $Q_3 - Q_1 = 75 - 45 =$ 30 [1] (b) (i) Class B (65 > 60). [1] (ii) Class A is more consistent because it has a smaller IQR (30 vs 25? Wait, Class A IQR=30, Class B IQR=20). Correction: Class B has smaller IQR (20 < 30). So Class B is more consistent. [2] Note: Lower IQR indicates less spread/more consistency.

8. (a) $Q_1$ represents 25% of data. $25\%$ of $100 =$ 25 plants. [1] (b) This is the interquartile range (50% of data). $50\%$ of $100 =$ 50 plants. [1] (c) Median represents 50%. Greater than median is the upper 50%. 50 plants. [1]

9. (a) IQR = $50 - 30 =$ 20 [1] (b) Threshold = $Q_3 + 1.5(\text{IQR}) = 50 + 1.5(20) = 50 + 30 =$ 80 [2]

10. Group X has a smaller IQR (10) compared to Group Y (25). This means the scores in Group X are more consistent (less spread out) around the median, while Group Y's scores are more varied. [2]

11. (a) Numbers > 4 are {5, 6}. $P = \frac{2}{6} =$ $\frac{1}{3}$ [1] (b) Even numbers are {2, 4, 6}. $P = \frac{3}{6} =$ $\frac{1}{2}$ [1]

12. Total balls = $5+3+2=10$ . (a) $P(\text{Red}) =$ $\frac{5}{10} = \frac{1}{2}$ [1] (b) $P(\text{Not Blue}) = 1 - P(\text{Blue}) = 1 - \frac{3}{10} =$ $\frac{7}{10}$ [1]

13. (a) Sample Space: {HH, HT, TH, TT} [1] (b) Exactly one head: {HT, TH}. $P = \frac{2}{4} =$ $\frac{1}{2}$ [1]

14. (a) Primes in 1-8: {2, 3, 5, 7}. Count = 4. $P = \frac{4}{8} =$ $\frac{1}{2}$ [2] (b) Multiples of 3: {3, 6}. Count = 2. $P = \frac{2}{8} =$ $\frac{1}{4}$ [1]

15. (a) Tree Diagram:

1st Draw: W (4/10), B (6/10)
2nd Draw (after W): W (3/9), B (6/9)
2nd Draw (after B): W (4/9), B (5/9) [2] (b) $P(WW) = \frac{4}{10} \times \frac{3}{9} = \frac{12}{90} =$ $\frac{2}{15}$ [2] (c) $P(\text{Different}) = P(WB) + P(BW) = (\frac{4}{10} \times \frac{6}{9}) + (\frac{6}{10} \times \frac{4}{9}) = \frac{24}{90} + \frac{24}{90} = \frac{48}{90} =$ $\frac{8}{15}$ [2]

16. (a) $P(\text{No Rain}) = 1 - 0.3 =$ 0.7 [1] (b) $P(\text{Rain and Rain}) = 0.3 \times 0.3 =$ 0.09 [2]

17. Total = 30. Neither = 5. So $n(M \cup P) = 25$ . $n(M) + n(P) - n(M \cap P) = 25$ $18 + 15 - n(M \cap P) = 25$ $33 - 25 = n(M \cap P) = 8$ . (a) Venn Diagram: Intersection = 8. M only = 10. P only = 7. Outside = 5. [2] (b) $P(M \cap P) = \frac{8}{30} =$ $\frac{4}{15}$ [2]

18. $A = \{2, 4, 6, 8, 10\}$ , $B = \{7, 8, 9, 10\}$ . (a) $P(A) = \frac{5}{10} =$ $\frac{1}{2}$ [1] (b) $A \cap B = \{8, 10\}$ . $P(A \cap B) = \frac{2}{10} =$ $\frac{1}{5}$ [1] (c) $A \cup B = \{2, 4, 6, 7, 8, 9, 10\}$ . Count = 7. $P(A \cup B) =$ $\frac{7}{10}$ [2] Alternatively: $P(A) + P(B) - P(A \cap B) = 0.5 + 0.4 - 0.2 = 0.7$ .

19. (a) $P(HHH) = 0.6 \times 0.6 \times 0.6 =$ 0.216 [1] (b) $P(\text{At least one T}) = 1 - P(\text{No T}) = 1 - P(HHH) = 1 - 0.216 =$ 0.784 [2]

20. (a) Sum of probabilities = 1. $0.5 + 0.3 + p = 1 \Rightarrow p =$ 0.2 [1] (b) $P(\text{Green and Green}) = 0.2 \times 0.2 =$ 0.04 [2]