Straighterline
Introduction to Statistics
Exam
1. What is the mean of the following data set: 4, 6, 8, 10, 12?
A. 6
B. 8
C. 9
D. 10
✅ Answer: B. 8
Explanation: (4 + 6 + 8 + 10 + 12) ÷ 5 = 40 ÷ 5 = 8.
2. The median of 2, 3, 5, 8, 10, 12 is:
A. 5
B. 6.5
C. 8
D. 7
✅ Answer: B. 6.5
Explanation: Even number of data points → median = average of 3rd and 4th terms =
(5 + 8)/2.
3. The mode of the data set 3, 3, 5, 7, 7, 7, 9 is:
A. 3
B. 7
C. 9
D. No mode
✅ Answer: B. 7
Explanation: 7 appears most frequently (3 times).
4. A dataset has a mean of 20 and a standard deviation of 4. What is the z-score of
the value 28?
,A. 1
B. 2
C. 3
D. 4
✅ Answer: B. 2
Explanation: z = (x - μ) / σ = (28 − 20) / 4 = 2.
5. Which of the following measures is most affected by outliers?
A. Median
B. Mode
C. Mean
D. Range
✅ Answer: C. Mean
Explanation: The mean shifts dramatically when extreme values are present.
Section 2: Probability
6. If you flip a fair coin three times, what is the probability of getting exactly two
heads?
A. 1/8
B. 3/8
C. 1/2
D. 5/8
✅ Answer: B. 3/8
Explanation: There are 8 outcomes, and 3 contain exactly 2 heads (HHT, HTH, THH).
7. A bag has 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a
blue marble?
A. 0.2
B. 0.3
C. 0.5
D. 0.8
, ✅ Answer: B. 0.3
Explanation: Total marbles = 10; blue = 3 → 3/10 = 0.3.
8. Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.5, find P(A ∩ B).
A. 0.1
B. 0.2
C. 0.25
D. 0.4
✅ Answer: B. 0.2
Explanation: For independent events: P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5.
Section 3: Probability Distributions
9. In a normal distribution, the mean = 100 and standard deviation = 10. What
percent of data lies between 90 and 110?
A. 34%
B. 68%
C. 95%
D. 99.7%
✅ Answer: B. 68%
Explanation: Within ±1 standard deviation = 68%.
10. The binomial distribution requires:
A. A fixed number of trials
B. Independent trials
C. Constant probability of success
D. All of the above
✅ Answer: D. All of the above
Section 4: Sampling and Confidence Intervals
Introduction to Statistics
Exam
1. What is the mean of the following data set: 4, 6, 8, 10, 12?
A. 6
B. 8
C. 9
D. 10
✅ Answer: B. 8
Explanation: (4 + 6 + 8 + 10 + 12) ÷ 5 = 40 ÷ 5 = 8.
2. The median of 2, 3, 5, 8, 10, 12 is:
A. 5
B. 6.5
C. 8
D. 7
✅ Answer: B. 6.5
Explanation: Even number of data points → median = average of 3rd and 4th terms =
(5 + 8)/2.
3. The mode of the data set 3, 3, 5, 7, 7, 7, 9 is:
A. 3
B. 7
C. 9
D. No mode
✅ Answer: B. 7
Explanation: 7 appears most frequently (3 times).
4. A dataset has a mean of 20 and a standard deviation of 4. What is the z-score of
the value 28?
,A. 1
B. 2
C. 3
D. 4
✅ Answer: B. 2
Explanation: z = (x - μ) / σ = (28 − 20) / 4 = 2.
5. Which of the following measures is most affected by outliers?
A. Median
B. Mode
C. Mean
D. Range
✅ Answer: C. Mean
Explanation: The mean shifts dramatically when extreme values are present.
Section 2: Probability
6. If you flip a fair coin three times, what is the probability of getting exactly two
heads?
A. 1/8
B. 3/8
C. 1/2
D. 5/8
✅ Answer: B. 3/8
Explanation: There are 8 outcomes, and 3 contain exactly 2 heads (HHT, HTH, THH).
7. A bag has 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a
blue marble?
A. 0.2
B. 0.3
C. 0.5
D. 0.8
, ✅ Answer: B. 0.3
Explanation: Total marbles = 10; blue = 3 → 3/10 = 0.3.
8. Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.5, find P(A ∩ B).
A. 0.1
B. 0.2
C. 0.25
D. 0.4
✅ Answer: B. 0.2
Explanation: For independent events: P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5.
Section 3: Probability Distributions
9. In a normal distribution, the mean = 100 and standard deviation = 10. What
percent of data lies between 90 and 110?
A. 34%
B. 68%
C. 95%
D. 99.7%
✅ Answer: B. 68%
Explanation: Within ±1 standard deviation = 68%.
10. The binomial distribution requires:
A. A fixed number of trials
B. Independent trials
C. Constant probability of success
D. All of the above
✅ Answer: D. All of the above
Section 4: Sampling and Confidence Intervals
