O Level Elementary Mathematics Statistics Probability Quiz

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O-Level Elementary Mathematics Quiz - Statistics Probability

Name: __________________________
Class: __________________________
Date: __________________________
Score: ________ / 45

Duration: 60 Minutes
Total Marks: 45

Instructions:

• Answer all questions.
• Give your answers to 3 significant figures unless specified otherwise.
• Show all essential working.
• Use of an approved scientific calculator is allowed.

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Section A: Data Handling and Analysis (Questions 1–12)

1. A set of data consists of the values: $12, 15, 12, 18, 22, 15, 12$. State the mode and the median of this data set. [2]

   Answer: __________________________

2. The mean of five numbers is 14. When a sixth number is added, the new mean becomes 15. Find the value of the sixth number. [2]

   Answer: __________________________

3. A stem-and-leaf diagram represents the heights of 20 students. The leaf values for the stem '16' are $2, 5, 5, 8$. How many students have a height between 162 cm and 165 cm (inclusive)? [1]

   Answer: __________________________

4. In a histogram, the class interval $20 < x \le 30$ has a frequency density of 1.2 students per unit. Calculate the frequency of students in this interval. [2]

   Answer: __________________________

5. A box-and-whisker plot shows a lower quartile of 35, a median of 50, and an upper quartile of 65. Calculate the interquartile range (IQR). [2]

   Answer: __________________________

6. Given a cumulative frequency curve, the total number of candidates is 120. Find the position of the lower quartile ($Q_1$) and the upper quartile ($Q_3$). [2]

   Answer: __________________________

7. A data set has a mean of 60 and a standard deviation of 4.5. If every value in the data set is increased by 5, state the new mean and the new standard deviation. [2]

   Answer: __________________________

8. The table below shows the marks of 10 students in a quiz:

   Mark	5	6	7	8	9
   Frequency	2	3	4	1	0
   Calculate the mean mark. [2]

   Answer: __________________________

9. Using the data from Question 8, calculate the standard deviation of the marks. [3]

   Answer: __________________________

10. Two sets of data, A and B, both have a mean of 75. The standard deviation of A is 3.2 and the standard deviation of B is 6.8. Which set is more consistent? Explain your answer. [2]

    Answer: __________________________

11. A pie chart represents the favorite sports of 180 students. The sector for "Football" has an angle of $108^\circ$. Calculate the number of students who chose Football. [2]

    Answer: __________________________

12. A graph shows the growth of a plant over 4 weeks. The y-axis starts at 10 cm instead of 0 cm. Explain why this feature might be considered misleading. [2]

    Answer: __________________________

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Section B: Probability (Questions 13–20)

13. A bag contains 5 red, 3 blue, and 2 green marbles. A marble is picked at random. Find the probability that it is NOT blue. [2]

    Answer: __________________________

14. Two fair six-sided dice are thrown. Find the probability that the sum of the two numbers is exactly 7. [2]

    Answer: __________________________

15. A coin is tossed twice. Draw a possibility diagram or list the sample space to find the probability of getting at least one head. [2]

    Answer: __________________________

16. Events $A$ and $B$ are mutually exclusive. Given $P(A) = 0.3$ and $P(B) = 0.4$, find $P(A \cup B)$. [2]

    Answer: __________________________

17. A box contains 4 red and 6 blue pens. Two pens are picked one after another without replacement. Find the probability that both pens are red. [3]

    Answer: __________________________

18. A box contains 4 red and 6 blue pens. Two pens are picked one after another with replacement. Find the probability that both pens are red. [2]

    Answer: __________________________

19. The probability that it rains on any given day in April is 0.3. Find the probability that it rains on exactly two consecutive days. [2]

    Answer: __________________________

20. A tree diagram is used to model a game where a player wins a prize with probability $\frac{1}{4}$ in the first round. If they lose, they can try a second round with a win probability of $\frac{1}{3}$. Calculate the probability that the player wins a prize. [4]

    Answer: __________________________

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Answer Key - Statistics Probability Quiz

1. Mode: 12 (appears 3 times). Median: 15 (ordered: 12, 12, 12, 15, 15, 18, 22). [2 marks]
2. Total of 5 numbers = $5 \times 14 = 70$. Total of 6 numbers = $6 \times 15 = 90$. Sixth number = $90 - 70 = 20$. [2 marks]
3. Values are 162, 165, 165, 168. Those between 162 and 165 inclusive are 162, 165, 165. Count = 3. [1 mark]
4. $\text{Frequency} = \text{Frequency Density} \times \text{Class Width} = 1.2 \times (30 - 20) = 12$. [2 marks]
5. $\text{IQR} = Q_3 - Q_1 = 65 - 35 = 30$. [2 marks]
6. $Q_1$ position: $0.25 \times 120 = 30\text{th}$ value. $Q_3$ position: $0.75 \times 120 = 90\text{th}$ value. [2 marks]
7. New Mean = $60 + 5 = 65$. New SD = 4.5 (SD remains unchanged when a constant is added to all values). [2 marks]
8. $\text{Mean} = \frac{(5\times2) + (6\times3) + (7\times4) + (8\times1)}{10} = \frac{10+18+28+8}{10} = \frac{64}{10} = 6.4$. [2 marks]
9. $\sum fx^2 = (25\times2) + (36\times3) + (49\times4) + (64\times1) = 50 + 108 + 196 + 64 = 422$. $\text{SD} = \sqrt{\frac{422}{10} - (6.4)^2} = \sqrt{42.2 - 40.96} = \sqrt{1.24} \approx 1.11$. [3 marks]
10. Set A is more consistent because it has a smaller standard deviation (3.2 < 6.8), meaning the data points are closer to the mean. [2 marks]
11. $\text{Number} = \frac{108}{360} \times 180 = 0.3 \times 180 = 54$ students. [2 marks]
12. The truncated y-axis (not starting at 0) exaggerates the visual difference in growth, making the increase appear more significant than it is. [2 marks]
13. $P(\text{Not Blue}) = 1 - P(\text{Blue}) = 1 - \frac{3}{10} = \frac{7}{10}$ or 0.7. [2 marks]
14. Sum of 7 outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Total outcomes = 36. $P = \frac{6}{36} = \frac{1}{6}$. [2 marks]
15. Sample space: {HH, HT, TH, TT}. At least one head: {HH, HT, TH}. $P = \frac{3}{4}$ or 0.75. [2 marks]
16. For mutually exclusive events, $P(A \cup B) = P(A) + P(B) = 0.3 + 0.4 = 0.7$. [2 marks]
17. $P(\text{Red}_1) = \frac{4}{10}$. $P(\text{Red}_2 | \text{Red}_1) = \frac{3}{9}$. $P = \frac{4}{10} \times \frac{3}{9} = \frac{12}{90} = \frac{2}{15} \approx 0.133$. [3 marks]
18. $P(\text{Red}_1) = \frac{4}{10}$. $P(\text{Red}_2) = \frac{4}{10}$. $P = \frac{4}{10} \times \frac{4}{10} = \frac{16}{100} = 0.16$. [2 marks]
19. $P(\text{Rain}) \times P(\text{Rain}) = 0.3 \times 0.3 = 0.09$. [2 marks]
20. $P(\text{Win}) = P(\text{Win 1st}) + P(\text{Lose 1st}) \times P(\text{Win 2nd})$ $P = \frac{1}{4} + (\frac{3}{4} \times \frac{1}{3}) = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}$ or 0.5. [4 marks]