Question 1

The marks scored by 7 students in a test are: 12, 18, 15, 22, 10, 18, 25. What is the mode of this data?

Accepted Answer

Step 1: List all values — 12, 18, 15, 22, 10, 18, 25. Step 2: Count the frequency of each value: 10→1, 12→1, 15→1, 18→2, 22→1, 25→1. Step 3: The value with the highest frequency is 18 (appears twice). Therefore, the mode is 18.

Question 2

The mean of five numbers is 24. If four of the numbers are 18, 22, 26, and 28, what is the fifth number?

Accepted Answer

Step 1: Use the formula Mean = (Sum of all numbers) / (Count of numbers). Step 2: Rearrange to find Sum = Mean × Count = 24 × 5 = 120. Step 3: Sum of four known numbers = 18 + 22 + 26 + 28 = 94. Step 4: Fifth number = 120 − 94 = 26. Therefore, the fifth number is 26.

Question 3

In how many ways can 5 different books be arranged on a shelf such that a specific book (say, Book A) is always at one of the end positions?

Accepted Answer

Step 1: Book A must occupy either the leftmost or rightmost position. There are 2 choices for placing Book A. Step 2: After placing Book A, the remaining 4 books can be arranged in the remaining 4 positions in 4! = 24 ways. Step 3: Total arrangements = 2 × 24 = 48.

Question 4

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random from the bag, what is the probability that it is neither red nor green?

Accepted Answer

Step 1: Total number of balls = 5 + 3 + 2 = 10. Step 2: Balls that are neither red nor green = blue balls = 3. Step 3: Probability = (Number of favourable outcomes) / (Total number of outcomes) = 3/10. Therefore, the answer is 3/10.

Question 5

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: Recall the property of variance under scaling. When each observation is multiplied by a constant k, the variance is multiplied by k². Step 2: Original variance = 36. Step 3: New variance = 36 × 5² = 36 × 25 = 900. Therefore, the answer is 900.

Question 6

In how many ways can 5 different books be arranged on a shelf such that a specific book (say, Book A) is always at one of the end positions?

Accepted Answer

Step 1: Book A must be at one of the two end positions. There are 2 choices for placing Book A (left end or right end). Step 2: The remaining 4 books can be arranged in the remaining 4 positions in 4! = 24 ways. Step 3: Total arrangements = 2 × 24 = 48.

Question 7

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: Recall the property of variance under linear transformation. When each observation is multiplied by a constant k, the variance is multiplied by k². Step 2: New variance = Original variance × k² = 36 × 5² = 36 × 25 = 900. Therefore, the answer is 900.

Question 8

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random from the bag, what is the probability that it is neither red nor green?

Accepted Answer

Step 1: Count total balls = 5 + 3 + 2 = 10 balls. Step 2: Identify favorable outcomes (neither red nor green) = blue balls = 3. Step 3: Apply probability formula: P(event) = Favorable outcomes / Total outcomes = 3/10. Therefore, the probability is 3/10 or 0.3.

Question 9

The mean of five numbers is 24. If four of the numbers are 18, 22, 26, and 28, what is the fifth number?

Accepted Answer

Step 1: Use the formula Mean = (Sum of all observations) / (Number of observations). Step 2: Rearrange to find Sum = Mean × Number of observations = 24 × 5 = 120. Step 3: Sum of four known numbers = 18 + 22 + 26 + 28 = 94. Step 4: Fifth number = 120 - 94 = 26.

Question 10

In how many ways can 5 different books be arranged on a shelf such that a specific book always remains in the middle position?

Accepted Answer

Step 1: Since one specific book must always be in the middle position (3rd position out of 5), its position is fixed and cannot be changed.
Step 2: The remaining 4 books can be arranged in the other 4 positions (1st, 2nd, 4th, and 5th) in any order.
Step 3: Number of ways to arrange 4 books in 4 positions = 4! = 4 × 3 × 2 × 1 = 24
Step 4: Since the middle position book is fixed, total arrangements = 1 × 24 = 24
Therefore, the answer is 24.

Question 11

For the dataset {1, 3, 5, 7, 9}, the standard deviation is closest to:

Accepted Answer

Step 1: Mean = (1 + 3 + 5 + 7 + 9) ÷ 5 = 25 ÷ 5 = 5. Step 2: Squared deviations: (1-5)² = 16, (3-5)² = 4, (5-5)² = 0, (7-5)² = 4, (9-5)² = 16. Step 3: Sum = 40. Step 4: Variance = 40 ÷ 5 = 8. Step 5: SD = √8 ≈ 2.83.

Question 12

A committee of 5 members is to be formed from a group of 6 men and 4 women. In how many ways can the committee be formed such that it contains at least 2 women?

Accepted Answer

Step 1: Identify valid compositions: at least 2 women means 2, 3, or 4 women. Step 2: Case 1 (2 women, 3 men): C(4,2) × C(6,3) = 6 × 20 = 120. Step 3: Case 2 (3 women, 2 men): C(4,3) × C(6,2) = 4 × 15 = 60. Step 4: Case 3 (4 women, 1 man): C(4,4) × C(6,1) = 1 × 6 = 6. Step 5: Total = 120 + 60 + 6 = 186.

Question 13

The mean of 8 numbers is 24. When a new number is added, the mean becomes 25. What is the new number that was added?

Accepted Answer

Step 1: Sum of original 8 numbers = Mean × Count = 24 × 8 = 192. Step 2: Sum of 9 numbers (after adding new number) = New Mean × Count = 25 × 9 = 225. Step 3: New number added = 225 − 192 = 33. Therefore, the answer is 33.

Question 14

A committee of 5 members is to be formed from a group of 6 men and 4 women. In how many ways can the committee be formed such that it contains at least 2 women?

Accepted Answer

Step 1: Identify valid compositions: at least 2 women means 2, 3, or 4 women. Step 2: Case 1 (2 women, 3 men): C(4,2) × C(6,3) = 6 × 20 = 120. Step 3: Case 2 (3 women, 2 men): C(4,3) × C(6,2) = 4 × 15 = 60. Step 4: Case 3 (4 women, 1 man): C(4,4) × C(6,1) = 1 × 6 = 6. Step 5: Total = 120 + 60 + 6 = 186.

Question 15

A bag contains 5 red balls, 7 blue balls, and 8 green balls. Two balls are drawn simultaneously at random from the bag. What is the probability that both balls are of different colours?

Accepted Answer

Step 1: Total balls = 5 + 7 + 8 = 20. Total ways to draw 2 balls = C(20,2) = 190. Step 2: Ways to draw both balls of same colour = C(5,2) + C(7,2) + C(8,2) = 10 + 21 + 28 = 59. Step 3: Ways to draw balls of different colours = 190 - 59 = 131. Step 4: Probability = 131/190. Therefore, answer is 131/190.

Question 16

The variance of a dataset is 36. If each observation in the dataset is multiplied by 5 and then 3 is subtracted from each result, what will be the new variance?

Accepted Answer

Step 1: Recall that when each observation is multiplied by a constant k, the variance is multiplied by k². Step 2: When a constant is added or subtracted, variance remains unchanged. Step 3: Original variance = 36. After multiplying by 5: new variance = 36 × 5² = 36 × 25 = 900. Step 4: Subtracting 3 does not change variance. Therefore, the new variance is 900.

Question 17

If each observation in a data set is multiplied by 3, and the standard deviation of the original data set is 4, what is the variance of the new data set?

Accepted Answer

Step 1: Recall the property — if each observation is multiplied by a constant k, the new standard deviation = k × original SD. Step 2: New SD = 3 × 4 = 12. Step 3: Variance = (SD)² = 12² = 144. Note: A common mistake is multiplying the original variance (16) by 3, giving 48, which is wrong. Therefore, answer is 144.

Question 18

A bag contains 4 red balls, 5 blue balls, and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are of the same colour?

Accepted Answer

Step 1: Total balls = 4 + 5 + 3 = 12. Total ways to choose 2 balls = C(12,2) = 66. Step 2: Favourable outcomes — both red: C(4,2) = 6; both blue: C(5,2) = 10; both green: C(3,2) = 3. Total favourable = 6 + 10 + 3 = 19. Step 3: Required probability = 19/66. Therefore, answer is 19/66.

Question 19

The variance of a dataset is 36. If each observation in the dataset is multiplied by 5 and then 3 is subtracted from each result, what will be the new variance?

Accepted Answer

Step 1: Recall that when each observation is multiplied by a constant k, the variance is multiplied by k². Step 2: When a constant is added or subtracted from each observation, variance remains unchanged. Step 3: Original variance = 36. After multiplying by 5: new variance = 36 × 5² = 36 × 25 = 900. Step 4: Subtracting 3 does not change variance. Therefore, the new variance is 900.

Question 20

In how many ways can the letters of the word 'GARDEN' be arranged such that the vowels always occupy the odd positions?

Accepted Answer

Step 1: Identify the letters in 'GARDEN' — G, A, R, D, E, N. Total 6 letters. Vowels: A, E (2 vowels). Consonants: G, R, D, N (4 consonants). Step 2: Odd positions in a 6-letter arrangement are positions 1, 3, 5 — that's 3 odd positions. We need to place 2 vowels in these 3 odd positions. Number of ways = P(3,2) = 3×2 = 6. Step 3: Remaining 4 consonants occupy the remaining 4 positions. Number of ways = 4! = 24. Step 4: Total arrangements = 6 × 24 = 144. Therefore, answer is 144.

SSC CGL Statistics Questions

SSC CGL Statistics — Past Exam Questions

Study by Subtopic — Statistics

Study Next — Quantitative Aptitude Topics