Question 1

For a dataset with mean 20 and standard deviation 5, what is the coefficient of variation (CV)?

Accepted Answer

Step 1: Coefficient of Variation (CV) = (Standard Deviation ÷ Mean) × 100%. Step 2: CV = (5 ÷ 20) × 100% = 0.25 × 100% = 25%.

Question 2

The variance of the dataset {2, 4, 6, 8, 10} is:

Accepted Answer

Step 1: Find the mean = (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6. Step 2: Find squared deviations from mean: (2−6)² = 16, (4−6)² = 4, (6−6)² = 0, (8−6)² = 4, (10−6)² = 16. Step 3: Sum of squared deviations = 16 + 4 + 0 + 4 + 16 = 40. Step 4: Variance = 40 ÷ 5 = 8.

Question 3

If the standard deviation of a dataset is 5, what is the variance?

Accepted Answer

Step 1: Recall that Variance = (Standard Deviation)². Step 2: Variance = 5² = 25.

Question 4

The standard deviation of the dataset {3, 3, 3, 3, 3} is:

Accepted Answer

Step 1: All values are identical (all equal to 3). Step 2: Mean = 3. Step 3: Every deviation from mean = 3 − 3 = 0. Step 4: Sum of squared deviations = 0. Step 5: Variance = 0 ÷ 5 = 0. Step 6: Standard Deviation = √0 = 0.

Question 5

The variance of {1, 2, 3, 4, 5} is 2. If each value is multiplied by 3, the new variance becomes:

Accepted Answer

Step 1: Recall the property: if each data point is multiplied by a constant k, the new variance = k² × (original variance). Step 2: Here, k = 3 and original variance = 2. Step 3: New variance = 3² × 2 = 9 × 2 = 18.

Question 6

The standard deviation of a dataset is 4. If a constant 10 is added to each value, the new standard deviation is:

Accepted Answer

Step 1: Recall the property: adding a constant to all data points does NOT change the standard deviation (or variance). Step 2: This is because adding a constant shifts all values equally, preserving the spread. Step 3: New standard deviation = 4.

Question 7

A fair coin is tossed 3 times. What is the probability of getting at least one head?

Accepted Answer

Step 1: Total possible outcomes when tossing a coin 3 times = 2³ = 8. Step 2: Outcomes with at least one head = Total outcomes - Outcomes with no heads (all tails). Step 3: Outcomes with all tails = 1 (TTT). Step 4: Outcomes with at least one head = 8 - 1 = 7. Step 5: Probability = 7/8.

Question 8

A number is chosen at random from the set {1, 2, 3, ..., 50}. What is the probability that the number is divisible by 3 or divisible by 5?

Accepted Answer

Step 1: Total numbers = 50. Step 2: Numbers divisible by 3: ⌊50/3⌋ = 16 (3, 6, 9, ..., 48). Step 3: Numbers divisible by 5: ⌊50/5⌋ = 10 (5, 10, 15, ..., 50). Step 4: Numbers divisible by both 3 and 5 (i.e., by 15): ⌊50/15⌋ = 3 (15, 30, 45). Step 5: Using inclusion-exclusion: 16 + 10 - 3 = 23. Step 6: Probability = 23/50.

Question 9

The variance of a dataset is 36. If each observation in the dataset is multiplied by 5, what will be the new variance?

Accepted Answer

Step 1: Original variance = 36. Step 2: When each observation is multiplied by a constant k, the new variance becomes k² × (original variance). Step 3: New variance = 5² × 36 = 25 × 36 = 900. Therefore, the answer is 900.

Question 10

The standard deviation of five numbers is 4. If the sum of the numbers is 50, what is the sum of their squares?

Accepted Answer

Step 1: Standard deviation σ = 4, so variance σ² = 16. Step 2: Mean = 50/5 = 10. Step 3: Variance formula: σ² = (Σx²)/n - (mean)². Step 4: 16 = (Σx²)/5 - 100. Step 5: (Σx²)/5 = 116. Step 6: Σx² = 580. Therefore, the answer is 580.

Question 11

Two datasets have the same mean of 20. Dataset A has a standard deviation of 3, and Dataset B has a standard deviation of 6. Which statement is correct?

Accepted Answer

Step 1: Both datasets have mean = 20. Step 2: Dataset A: σ_A = 3, so variance = 9. Step 3: Dataset B: σ_B = 6, so variance = 36. Step 4: Since variance of B (36) > variance of A (9), Dataset B has greater spread/dispersion around the mean. Step 5: Dataset B is more dispersed/variable. Therefore, the answer is that Dataset B has greater variability.

Question 12

The variance of the dataset {2, 4, 6, 8, 10} is calculated. If a constant 3 is added to each observation, what is the change in variance?

Accepted Answer

Step 1: When a constant is added to each observation, the mean shifts by that constant, but the deviations from the mean remain unchanged. Step 2: Variance depends only on deviations from the mean, not on the absolute values. Step 3: Adding a constant does not change variance. Step 4: Change in variance = 0. Therefore, the answer is 0.

Question 13

A dataset has 10 observations with a mean of 15 and a sum of squared deviations from the mean of 400. What is the standard deviation?

Accepted Answer

Step 1: Sum of squared deviations = 400. Step 2: Variance = (Sum of squared deviations) / n = 400 / 10 = 40. Step 3: Standard deviation = √variance = √40 = √(4 × 10) = 2√10 ≈ 6.32. However, checking for clean answers: √40 = 2√10. Step 4: If the problem expects a simplified form, SD = 2√10. If numerical: SD ≈ 6.32. For SSC exams, the answer is typically 2√10 or approximately 6.32. Therefore, the answer is 2√10.

Question 14

How many 4-digit numbers can be formed using the digits 2, 3, 4, 5, 6 without repetition such that the number is divisible by 5?

Accepted Answer

Step 1: For divisibility by 5, the last digit must be 5 (only digit divisible by 5 in the set). Step 2: Fix 5 at the units place. Step 3: Fill the remaining 3 positions with 3 digits chosen from {2, 3, 4, 6}. This is P(4,3) = 4 × 3 × 2 = 24.

Question 15

A committee of 4 people is to be selected from 6 men and 5 women. In how many ways can this be done if the committee must have at least 2 women?

Accepted Answer

Step 1: 'At least 2 women' means 2 women or 3 women or 4 women. Step 2: Case 1 (2W, 2M): C(5,2) × C(6,2) = 10 × 15 = 150. Step 3: Case 2 (3W, 1M): C(5,3) × C(6,1) = 10 × 6 = 60. Step 4: Case 3 (4W, 0M): C(5,4) × C(6,0) = 5 × 1 = 5. Step 5: Total = 150 + 60 + 5 = 215.

Question 16

In how many ways can the letters of the word 'MISSISSIPPI' be arranged?

Accepted Answer

Step 1: Count total letters: M(1), I(4), S(4), P(2) = 11 letters total. Step 2: Use formula for permutations with repetition: n! / (n₁! × n₂! × ... × nₖ!). Step 3: Arrangements = 11! / (1! × 4! × 4! × 2!) = 39916800 / (1 × 24 × 24 × 2) = 39916800 / 1152 = 34650.

Question 17

How many ways can 3 prizes be distributed among 8 students if each student can receive at most one prize?

Accepted Answer

Step 1: We need to select 3 students from 8 to receive the 3 distinct prizes. Step 2: Since prizes are distinct, order matters. Step 3: This is a permutation problem: P(8,3) = 8!/(8-3)! = 8!/5! = 8 × 7 × 6 = 336.

Question 18

A group of 10 people consists of 6 men and 4 women. In how many ways can a team of 5 people be formed such that it has more men than women?

Accepted Answer

Step 1: 'More men than women' in a 5-person team means: (4M, 1W) or (5M, 0W). Step 2: Case 1 (4M, 1W): C(6,4) × C(4,1) = 15 × 4 = 60. Step 3: Case 2 (5M, 0W): C(6,5) × C(4,0) = 6 × 1 = 6. Step 4: Total = 60 + 6 = 66.

Question 19

A bag contains 5 red balls, 7 blue balls, and 8 green balls. If one ball is drawn at random, what is the probability that it is neither red nor green?

Accepted Answer

Step 1: Total balls = 5 + 7 + 8 = 20. Step 2: Balls that are neither red nor green = blue balls = 7. Step 3: Probability = 7/20.

Question 20

The standard deviation of a dataset is 5. If each observation is decreased by 2 and then multiplied by 3, what is the new standard deviation?

Accepted Answer

Step 1: Original standard deviation σ = 5. Step 2: Subtracting a constant does not change standard deviation (only shifts the mean). Step 3: After subtracting 2: new σ = 5. Step 4: Multiplying by 3 scales the standard deviation by the absolute value of the multiplier. Step 5: New σ = 3 × 5 = 15. Therefore, the answer is 15.

SSC GD Constable Statistics Questions

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