College Exam Quiz Questions Statistics and Probability sample multiple‐choice questions—
with answers and brief explanations—covering key concepts in Statistics and Probability. Use
these questions to review topics from descriptive statistics and probability fundamentals to
distributions, hypothesis testing, and more.
1. Descriptive Statistics – Mean
Find the mean of the data set: {4, 8, 10, 12}.
A) 8 B) 8.5 C) 9 D) 9.5
Answer: B) 8.5
Explanation: Mean = (4 + 8 + 10 + 12) / 4 = 34/4 = 8.5.
2. Descriptive Statistics – Median
Find the median of the data set: {7, 2, 9, 4, 6}.
A) 4 B) 6 C) 7 D) 9
Answer: B) 6
Explanation: Ordering the set gives {2, 4, 6, 7, 9}. The middle value is 6.
3. Descriptive Statistics – Mode
Find the mode of the data set: {5, 3, 8, 5, 10, 8, 5}.
A) 3 B) 5 C) 8 D) 10
Answer: B) 5
Explanation: The value 5 occurs three times, more than any other value.
4. Variance (Population)
What is the population variance of the data set: {2, 4, 6, 8}?
A) 4 B) 5 C) 6 D) 7
Answer: B) 5
Explanation: Mean = 5; squared deviations: (2–5)²=9, (4–5)²=1, (6–5)²=1, (8–5)²=9; Sum =
20; Variance = 20/4 = 5.
5. Standard Deviation (Population)
What is the population standard deviation of the data set: {2, 4, 6, 8}?
A) 2 B) 2.236 C) 2.5 D) 3
Answer: B) 2.236
Explanation: Standard deviation = √(Variance) = √5 ≈ 2.236.
, 6. Two Dice – Sum Probability
What is the probability of rolling a sum of 7 with two fair six-sided dice?
A) 1/6 B) 1/8 C) 1/9 D) 1/12
Answer: A) 1/6
Explanation: There are 6 favorable outcomes (1–6, 2–5, 3–4, 4–3, 5–2, 6–1) out of 36 total
outcomes.
7. Card Probability
What is the probability of drawing an ace from a standard 52-card deck?
A) 1/12 B) 1/13 C) 1/14 D) 1/15
Answer: B) 1/13
Explanation: There are 4 aces, so probability = 4/52 = 1/13.
8. Coin Flips – Outcome Count
How many possible outcomes are there when flipping 3 coins?
A) 6 B) 7 C) 8 D) 9
Answer: C) 8
Explanation: Each coin has 2 outcomes, so 2³ = 8 total outcomes.
9. Combinations
How many ways can you choose 3 items from a set of 10?
A) 60 B) 120 C) 210 D) 720
Answer: B) 120
Explanation: Using the combination formula, C(10, 3) = 10!/(3!·7!) = 120.
10. Permutations
How many ways can you arrange 3 out of 10 items?
A) 120 B) 210 C) 720 D) 840
Answer: C) 720
Explanation: Using the permutation formula, P(10, 3) = 10 × 9 × 8 = 720.
11. Independent Events
If events A and B are independent with P(A) = 0.5 and P(B) = 0.3, what is P(A and B)?
A) 0.15 B) 0.8 C) 0.5 D) 0.3
with answers and brief explanations—covering key concepts in Statistics and Probability. Use
these questions to review topics from descriptive statistics and probability fundamentals to
distributions, hypothesis testing, and more.
1. Descriptive Statistics – Mean
Find the mean of the data set: {4, 8, 10, 12}.
A) 8 B) 8.5 C) 9 D) 9.5
Answer: B) 8.5
Explanation: Mean = (4 + 8 + 10 + 12) / 4 = 34/4 = 8.5.
2. Descriptive Statistics – Median
Find the median of the data set: {7, 2, 9, 4, 6}.
A) 4 B) 6 C) 7 D) 9
Answer: B) 6
Explanation: Ordering the set gives {2, 4, 6, 7, 9}. The middle value is 6.
3. Descriptive Statistics – Mode
Find the mode of the data set: {5, 3, 8, 5, 10, 8, 5}.
A) 3 B) 5 C) 8 D) 10
Answer: B) 5
Explanation: The value 5 occurs three times, more than any other value.
4. Variance (Population)
What is the population variance of the data set: {2, 4, 6, 8}?
A) 4 B) 5 C) 6 D) 7
Answer: B) 5
Explanation: Mean = 5; squared deviations: (2–5)²=9, (4–5)²=1, (6–5)²=1, (8–5)²=9; Sum =
20; Variance = 20/4 = 5.
5. Standard Deviation (Population)
What is the population standard deviation of the data set: {2, 4, 6, 8}?
A) 2 B) 2.236 C) 2.5 D) 3
Answer: B) 2.236
Explanation: Standard deviation = √(Variance) = √5 ≈ 2.236.
, 6. Two Dice – Sum Probability
What is the probability of rolling a sum of 7 with two fair six-sided dice?
A) 1/6 B) 1/8 C) 1/9 D) 1/12
Answer: A) 1/6
Explanation: There are 6 favorable outcomes (1–6, 2–5, 3–4, 4–3, 5–2, 6–1) out of 36 total
outcomes.
7. Card Probability
What is the probability of drawing an ace from a standard 52-card deck?
A) 1/12 B) 1/13 C) 1/14 D) 1/15
Answer: B) 1/13
Explanation: There are 4 aces, so probability = 4/52 = 1/13.
8. Coin Flips – Outcome Count
How many possible outcomes are there when flipping 3 coins?
A) 6 B) 7 C) 8 D) 9
Answer: C) 8
Explanation: Each coin has 2 outcomes, so 2³ = 8 total outcomes.
9. Combinations
How many ways can you choose 3 items from a set of 10?
A) 60 B) 120 C) 210 D) 720
Answer: B) 120
Explanation: Using the combination formula, C(10, 3) = 10!/(3!·7!) = 120.
10. Permutations
How many ways can you arrange 3 out of 10 items?
A) 120 B) 210 C) 720 D) 840
Answer: C) 720
Explanation: Using the permutation formula, P(10, 3) = 10 × 9 × 8 = 720.
11. Independent Events
If events A and B are independent with P(A) = 0.5 and P(B) = 0.3, what is P(A and B)?
A) 0.15 B) 0.8 C) 0.5 D) 0.3
