All Free Quantitative Methods MCQs with Answers

• A. 9.5
• B. 10.5
• C. 11.5
• D. 12.5

Explanation: After arranging the values, the middle two observations are 9 and 12. Since there are six observations, the median is their average, which…

• A. When all observations are distinct
• B. When all observations are equal
• C. When the median is zero
• D. When the range is maximum

Explanation: The arithmetic mean equals the geometric mean when every positive observation has the same value.

• A. 2
• B. Square root of 10
• C. 3
• D. Square root of 5

Explanation: The mean is 7, and the squared deviations are 9, 1, 1 and 9. Their population average is 5, so the population standard deviation is the…

• A. 2.0
• B. 2.4
• C. 3.0
• D. 3.2

Explanation: The median is 6. The absolute deviations from 6 total 12, and dividing by the five observations gives a mean deviation of 2.4.

• A. 5
• B. 6
• C. 12
• D. 24

Explanation: The semi-interquartile range is half the difference between the third and first quartiles. Thus, it is (18 minus 6) divided by 2, or 6.

• A. Variance
• B. Coefficient of variation
• C. Standard deviation
• D. Squared range

Explanation: Standard deviation is the square root of variance, so it retains the original measurement units.

• A. 50 percent
• B. 60 percent
• C. 75 percent
• D. 95 percent

Explanation: Chebyshev's theorem gives the minimum proportion as 1 minus 1 divided by k squared. For k equal to 2, this is 1 minus 1/4, or 75 percent.

• A. n
• B. n minus 1
• C. n plus 1
• D. 2n

Explanation: The sample variance uses n minus 1 in the denominator to correct for the loss of one degree of freedom when the sample mean is estimated.

• A. Mean is below median and mode
• B. Mean is above median and mode
• C. Mean, median and mode are equal
• D. Mean equals mode but not median

Explanation: A perfectly symmetrical unimodal distribution has its centre at the same point for all three measures.

• A. Arithmetic mean
• B. Median
• C. Geometric mean
• D. Mode

Explanation: Nominal categories have no meaningful numerical order or distance, so their most frequent category is summarized by the mode.

• A. 0.10
• B. 0.28
• C. 0.70
• D. 1.20

Explanation: For mutually exclusive events, the events cannot occur together, so P(A ∪ B) = P(A) + P(B).

• A. 3/8
• B. 5/8
• C. 3/5
• D. 5/3

Explanation: Since every ball is either red or blue, not blue means red in this bag.

• A. 0.400
• B. 0.625?
• C. 0.625
• D. 0.500

Explanation: Using Bayes' theorem, P(B | defective) = (0.40 × 0.05) divided by [(0.60 × 0.02) + (0.40 × 0.05)] = 0.625.

• A. 3/8
• B. 1/4
• C. 1/8
• D. 1/2

Explanation: This follows a binomial distribution with n = 4, p = 1/2, and r = 2. The probability is C(4,2)(1/2)^2(1/2)^2 = 6/16 = 3/8.

• A. 3
• B. 6
• C. 7
• D. 20

Explanation: The mean of a binomial distribution is np. Therefore, E(X) = 20 × 0.3 = 6, while 20 is the number of trials rather than the expected…

• A. 2
• B. 4
• C. 8
• D. 16

Explanation: For a Poisson distribution, both the mean and the variance equal λ. Hence, when λ = 4, the variance is also 4.

• A. 2.10
• B. 2.40
• C. 2.70
• D. 3.00

Explanation: The expected value is found by multiplying each value by its probability and adding the results: (1 × 0.2) + (2 × 0.5) + (4 × 0.3) = 2.4.

• A. 0.032
• B. 0.128
• C. 0.160
• D. 0.200

Explanation: The first two attempts must fail and the third must succeed. Thus, the probability is (0.8)^2 × 0.2 = 0.128, which is the geometric…

• A. 0.025
• B. 0.250
• C. 0.500
• D. 0.975

Explanation: The standard normal distribution is symmetric about zero, and zero is its mean and median.

• A. 0.10
• B. 0.30
• C. 0.55
• D. 1.10

Explanation: For independent events, the probability of their intersection equals the product of their probabilities.