All Free Quantitative Methods MCQs with Answers

• A. 9
• B. 10
• C. 11
• D. 12

Explanation: The arithmetic mean is found by adding all values and dividing by their number. Their sum is 50, and 50 divided by 5 equals 10.

• A. 9
• B. 10.5
• C. 12
• D. 15

Explanation: The data are already arranged in ascending order. Since there are seven values, the fourth value is the middle value, so the median is 12.

• A. 3
• B. 5
• C. 7
• D. 8

Explanation: The mode is the value that occurs most frequently. The number 5 appears three times, while every other value appears once.

• A. 70
• B. 72
• C. 73
• D. 75

Explanation: The weighted mean is calculated as 60(0.20) + 70(0.30) + 80(0.50). This gives 12 + 21 + 40 = 73, unlike the simple mean, which gives equal…

• A. 4
• B. 5
• C. 6
• D. 20

Explanation: The mean is 5, and the squared deviations are 9, 1, 1 and 9, giving a total of 20.

• A. It remains unchanged
• B. It decreases by 10
• C. It increases by 10
• D. It becomes 10 times larger

Explanation: Adding the same constant shifts every observation and the mean by the same amount.

• A. 5%
• B. 10%
• C. 20%
• D. 25%

Explanation: The coefficient of variation is calculated as standard deviation divided by mean, multiplied by 100. Thus, (5/50) × 100 = 10%.

• A. 6
• B. 8
• C. 10
• D. 12

Explanation: The lower half is 3, 5, 7 and 9, whose median is 6, so Q1 equals 6. The upper half has median 14, so Q3 equals 14 and the interquartile…

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

Explanation: The median depends on the position of observations rather than their numerical distance from the centre.

• A. 20
• B. 21
• C. 22
• D. 24

Explanation: The combined total is (20 × 15) + (30 × 25) = 1,050, and the combined number of observations is 50.

• A. 4
• B. 6
• C. 8
• D. 12

Explanation: The geometric mean is the cube root of the product: (2 × 8 × 32)^(1/3) = 512^(1/3) = 8.

• A. 2.5
• B. 3
• C. 4
• D. 4.5

Explanation: For two values, the harmonic mean is 2ab/(a + b). Thus, it is 2(2)(6)/(2 + 6) = 24/8 = 3.

• A. 14
• B. 16
• C. 18
• D. 20

Explanation: The range equals the largest value minus the smallest value. Therefore, range = 25 − 7 = 18, not the difference between any two middle…

• A. 2
• B. 3
• C. 4
• D. 6

Explanation: The mean is 5, and the squared deviations are 4, 0 and 4. Their sum is 8, which is divided by n − 1, or 2, for a sample variance of 4.

• A. Mean 40, standard deviation 4
• B. Mean 60, standard deviation 6
• C. Mean 80, standard deviation 12
• D. Mean 100, standard deviation 9

Explanation: Relative variability is compared using the coefficient of variation. The coefficients are 10%, 10%, 15% and 9%, respectively, so the third…

• A. 1
• B. 8/3
• C. 2
• D. 4/3

Explanation: The mean is 4, and the absolute deviations are 2, 0 and 2. Their total is 4, so the mean deviation is 4/3.

• A. Mean < median < mode
• B. Mode < median < mean
• C. Mean = median = mode
• D. Median < mean < mode

Explanation: A positively skewed distribution has a long tail toward larger values, which pulls the mean to the right.

• A. 0.25
• B. 0.40
• C. 0.50
• D. 0.67

Explanation: The coefficient of range is (largest − smallest)/(largest + smallest). Thus, it is (30 − 10)/(30 + 10) = 20/40 = 0.50.

• A. It becomes one-third as large
• B. It remains unchanged
• C. It becomes three times as large
• D. It becomes negative three times as large

Explanation: Standard deviation is multiplied by the absolute value of the multiplying constant.

• A. 24
• B. 26
• C. 28
• D. 30

Explanation: Substituting the values gives Mode = 3(22) − 2(20) = 66 − 40 = 26. This is an empirical approximation used for moderately skewed…