Q.1 The mean of the numbers 5, 8, 12, 20, and 25 is:
12
14
15
16
Explanation - Mean = (5+8+12+20+25)/5 = 70/5 = 14.
Correct answer is: 14
Q.2 If the median of 7, 3, 9, 12, 5 is x, then x equals:
5
7
9
6
Explanation - Arrange in ascending order: 3, 5, 7, 9, 12. Median is the middle value = 7.
Correct answer is: 7
Q.3 The mode of 2, 4, 4, 5, 6, 4, 7 is:
4
5
6
7
Explanation - Mode is the number that occurs most frequently. Here, 4 occurs 3 times.
Correct answer is: 4
Q.4 The variance of the data 2, 4, 6, 8 is:
5
6.6667
8
4.5
Explanation - Mean = (2+4+6+8)/4 = 5. Variance = [(2-5)^2 + (4-5)^2 + (6-5)^2 + (8-5)^2]/4 = (9+1+1+9)/4 = 20/4 = 5.
Correct answer is: 5
Q.5 If two dice are rolled, the probability that the sum is 7 is:
1/6
1/8
1/12
1/36
Explanation - Favorable outcomes: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1). Total outcomes = 36. Probability = 6/36 = 1/6.
Correct answer is: 1/6
Q.6 The standard deviation of the numbers 3, 7, 7, 19 is:
6
5
4
3
Explanation - Mean = (3+7+7+19)/4 = 36/4 = 9. Variance = [(3-9)^2 + (7-9)^2 + (7-9)^2 + (19-9)^2]/4 = (36+4+4+100)/4 = 144/4 = 36. Std deviation = √36 = 6.
Correct answer is: 6
Q.7 The sum of deviations of all observations from their mean is always:
Positive
Negative
Zero
Cannot be determined
Explanation - By definition, sum of deviations from the mean Σ(xi - x̄) = 0.
Correct answer is: Zero
Q.8 The coefficient of variation (CV) is defined as:
Variance/Mean
Standard deviation/Mean
Mean/Standard deviation
Mean × Standard deviation
Explanation - Coefficient of variation = (σ/μ) × 100%.
Correct answer is: Standard deviation/Mean
Q.9 If the probability of an event is 0.2, its complementary event has probability:
0.8
0.2
0.5
0.6
Explanation - Probability of complementary event = 1 - P(event) = 1 - 0.2 = 0.8.
Correct answer is: 0.8
Q.10 A random variable X takes values 1, 2, 3 with probabilities 0.2, 0.5, 0.3. The expected value E(X) is:
2
1.9
2.1
2.5
Explanation - E(X) = Σ [x * P(x)] = 1*0.2 + 2*0.5 + 3*0.3 = 0.2 + 1 + 0.9 = 2.
Correct answer is: 2
Q.11 The probability distribution where all outcomes are equally likely is called:
Binomial
Uniform
Poisson
Normal
Explanation - In a uniform distribution, all outcomes have equal probability.
Correct answer is: Uniform
Q.12 The median of a continuous frequency distribution is calculated by:
Mode formula
Mean formula
Using cumulative frequency
Variance formula
Explanation - Median is found using the formula involving the cumulative frequency up to the median class.
Correct answer is: Using cumulative frequency
Q.13 In a normal distribution, approximately what percent of data lies within one standard deviation from the mean?
68%
50%
95%
99.7%
Explanation - Empirical rule: 68% within 1σ, 95% within 2σ, 99.7% within 3σ.
Correct answer is: 68%
Q.14 If events A and B are independent, then P(A ∩ B) equals:
P(A) + P(B)
P(A) × P(B)
P(A) - P(B)
P(A)/P(B)
Explanation - For independent events, probability of intersection = product of individual probabilities.
Correct answer is: P(A) × P(B)
Q.15 The sum of probabilities of all outcomes in a probability distribution is:
0
1
Greater than 1
Cannot be determined
Explanation - Sum of probabilities in any probability distribution must equal 1.
Correct answer is: 1
Q.16 The probability of getting exactly 2 heads in 3 tosses of a fair coin is:
1/8
3/8
1/2
3/4
Explanation - Number of favorable outcomes: HHT, HTH, THH = 3. Total outcomes = 8. Probability = 3/8.
Correct answer is: 3/8
Q.17 If variance of X is 16, standard deviation of X is:
2
4
8
16
Explanation - Standard deviation = √variance = √16 = 4.
Correct answer is: 4
Q.18 For a dataset, the sum of squared deviations from the mean divided by n is called:
Standard deviation
Variance
Mean deviation
Coefficient of variation
Explanation - Variance = Σ(xi - x̄)² / n.
Correct answer is: Variance
Q.19 The shape of the probability distribution for a fair die roll is:
Normal
Uniform
Binomial
Poisson
Explanation - All outcomes (1 to 6) are equally likely, so it's uniform.
Correct answer is: Uniform
Q.20 If two events are mutually exclusive, then P(A ∪ B) equals:
P(A) × P(B)
P(A) + P(B)
P(A) - P(B)
P(A)/P(B)
Explanation - For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).
Correct answer is: P(A) + P(B)
Q.21 The probability of drawing an ace from a standard deck of 52 cards is:
1/52
1/13
4/52
1/4
Explanation - Number of aces = 4, total cards = 52. Probability = 4/52 = 1/13.
Correct answer is: 1/13
Q.22 The median of 1, 2, 3, 4, 5, 6, 7, 8 is:
4
4.5
5
5.5
Explanation - Even number of observations, median = average of 4th and 5th values = (4+5)/2 = 4.5.
Correct answer is: 4.5
Q.23 If a probability density function f(x) is uniform over [0,1], the expected value E(X) is:
0.25
0.5
0.75
1
Explanation - For uniform[0,1], E(X) = (a+b)/2 = (0+1)/2 = 0.5.
Correct answer is: 0.5
Q.24 The probability of at least one success in n independent Bernoulli trials is:
(1-p)^n
1 - (1-p)^n
p^n
1 - p^n
Explanation - Probability of at least one success = 1 - P(no success) = 1 - (1-p)^n.
Correct answer is: 1 - (1-p)^n