Question 1

In how many ways can 5 different books be arranged on a shelf?

Accepted Answer

Step 1: We need to arrange 5 different books in a line. Step 2: This is a permutation problem where all 5 objects are used: P(5,5) = 5! = 5 × 4 × 3 × 2 × 1 = 120. Therefore, the answer is 120.

Question 2

The median of the dataset: 12, 18, 15, 22, 20 is ___. (Arrange in order first)

Accepted Answer

Step 1: Arrange in ascending order: 12, 15, 18, 20, 22. Step 2: Count = 5 (odd number). Step 3: Median position = (5 + 1) ÷ 2 = 3rd position. Step 4: The 3rd value is 18. Therefore, the median is 18.

Question 3

The marks obtained by 5 students in a test are: 45, 52, 48, 52, 63. What is the mean of their marks?

Accepted Answer

Step 1: Sum of all marks = 45 + 52 + 48 + 52 + 63 = 260. Step 2: Mean = Sum ÷ Number of students = 260 ÷ 5 = 52. Therefore, the mean is 52.

Question 4

A dataset has values: 5, 8, 8, 8, 12, 15. The mean is 9.33 (approx). What is the mode?

Accepted Answer

Step 1: Identify the frequency of each value: 5 appears 1 time, 8 appears 3 times, 12 appears 1 time, 15 appears 1 time. Step 2: The mode is the value with the highest frequency. Step 3: 8 appears 3 times (most frequent). Therefore, the mode is 8.

Question 5

The ages of 7 employees are arranged in ascending order: 22, 24, 26, 28, 30, 32, 34. What is the median age?

Accepted Answer

Step 1: Count the number of observations = 7 (odd number). Step 2: Median position = (7 + 1) ÷ 2 = 4th position. Step 3: The 4th value in the ordered list is 28. Therefore, the median age is 28.

Question 6

The mean of 6 numbers is 24. If five of the numbers are 18, 22, 26, 28, and 30, what is the sixth number?

Accepted Answer

Step 1: Mean = Sum of all numbers ÷ Count. Step 2: 24 = Sum ÷ 6, so Sum = 24 × 6 = 144. Step 3: Sum of five known numbers = 18 + 22 + 26 + 28 + 30 = 124. Step 4: Sixth number = 144 − 124 = 20. Therefore, the sixth number is 20.

Question 7

In a dataset of 8 values: 10, 15, 15, 20, 20, 20, 25, 30, what is the mode?

Accepted Answer

Step 1: Count the frequency of each value: 10 appears 1 time, 15 appears 2 times, 20 appears 3 times, 25 appears 1 time, 30 appears 1 time. Step 2: The mode is the value with the highest frequency. Step 3: 20 appears 3 times (most frequent). Therefore, the mode is 20.

Question 8

How many ways can a committee of 3 people be selected from a group of 8 people?

Accepted Answer

Step 1: We need to select 3 people from 8 where order does not matter. Step 2: This is a combination problem: C(8,3) = 8!/(3! × 5!) = (8 × 7 × 6)/(3 × 2 × 1) = 336/6 = 56. Therefore, the answer is 56.

Question 9

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

Accepted Answer

Step 1: The word 'APPLE' has 5 letters with 'P' repeated twice. Step 2: When objects are repeated, we use: n!/(n₁! × n₂! × ...). Step 3: Arrangements = 5!/2! = (5 × 4 × 3 × 2 × 1)/2 = 120/2 = 60. Therefore, the answer is 60.

Question 10

How many 2-digit numbers can be formed using the digits 2, 3, 4, 5 without repetition?

Accepted Answer

Step 1: We need to form 2-digit numbers using 4 different digits without repetition. Step 2: For the first position, we have 4 choices. For the second position, we have 3 remaining choices. Step 3: Total = 4 × 3 = 12. Alternatively, P(4,2) = 4!/(4-2)! = 4!/2! = 12. Therefore, the answer is 12.

Question 11

In how many ways can 4 red balls and 3 blue balls be arranged in a line?

Accepted Answer

Step 1: We have 7 balls total: 4 identical red balls and 3 identical blue balls. Step 2: When arranging objects with repetitions, we use: n!/(n₁! × n₂!). Step 3: Arrangements = 7!/(4! × 3!) = (7 × 6 × 5 × 4!)/(4! × 3 × 2 × 1) = (7 × 6 × 5)/6 = 35. Therefore, the answer is 35.

Question 12

How many ways can 6 students be divided into two groups of 3 each?

Accepted Answer

Step 1: We need to divide 6 students into two indistinguishable groups of 3 each. Step 2: If we select 3 students for the first group, the remaining 3 automatically form the second group. Step 3: Initial selection = C(6,3) = 20. Step 4: Since the two groups are indistinguishable (dividing, not arranging), we divide by 2!: 20/2 = 10. Therefore, the answer is 10.

Question 13

How many 4-digit numbers can be formed using the digits 1, 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 (since 0 is not available). Step 2: Fix 5 in the units place. Step 3: Now we need to fill the first 3 positions with digits from {1, 2, 3, 4, 6} without repetition. Step 4: Number of ways = P(5,3) = 5 × 4 × 3 = 60.

Question 14

From a deck of 52 playing cards, in how many ways can 5 cards be selected such that there are exactly 2 cards of one suit and exactly 3 cards of another suit?

Accepted Answer

Step 1: Choose 2 suits from 4 suits: C(4,2) = 6 ways. Step 2: Decide which suit gets 2 cards and which gets 3 cards: 2 ways (suit A has 2 and suit B has 3, or vice versa). Step 3: Select 2 cards from the first chosen suit: C(13,2) = 78. Step 4: Select 3 cards from the second chosen suit: C(13,3) = 286. Step 5: Total = 6 × 2 × 78 × 286 = 268,656.

Question 15

In how many ways can 5 different books be arranged on a shelf such that two specific books are always together?

Accepted Answer

Step 1: Treat the two specific books as a single unit. Now we have 4 units to arrange (the combined unit + 3 other books). Step 2: These 4 units can be arranged in 4! = 24 ways. Step 3: The two books within their unit can be arranged among themselves in 2! = 2 ways. Step 4: Total arrangements = 24 × 2 = 48.

Question 16

A committee of 4 members 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 (2 women, 2 men): C(5,2) × C(6,2) = 10 × 15 = 150. Step 3: Case 2 (3 women, 1 man): C(5,3) × C(6,1) = 10 × 6 = 60. Step 4: Case 3 (4 women, 0 men): C(5,4) × C(6,0) = 5 × 1 = 5. Step 5: Total = 150 + 60 + 5 = 215.

Question 17

In a group of 8 students, a team of 3 is to be selected for a project. Additionally, from the remaining 5 students, 2 must be chosen as alternates. In how many ways can this be done?

Accepted Answer

Step 1: Select 3 students from 8 for the main team: C(8,3) = 56. Step 2: From the remaining 5 students, select 2 as alternates: C(5,2) = 10. Step 3: Total ways = 56 × 10 = 560.

Question 18

The mean of 8 numbers is 24. If one number is replaced by 40, the new mean becomes 27. What was the original number that was replaced?

Accepted Answer

Step 1: Sum of original 8 numbers = 8 × 24 = 192. Step 2: Sum of new 8 numbers = 8 × 27 = 216. Step 3: Difference = 216 − 192 = 24. Step 4: Original number = 40 − 24 = 16.

Question 19

The mode of a dataset is 28, and it appears 5 times. The second most frequent value is 35, appearing 3 times. If the dataset has 20 observations total, and all other values appear exactly once, how many distinct values are in the dataset?

Accepted Answer

Step 1: Mode (28) appears 5 times. Step 2: Second most frequent value (35) appears 3 times. Step 3: Total observations accounted for = 5 + 3 = 8. Step 4: Remaining observations = 20 − 8 = 12. Step 5: All remaining values appear exactly once, so there are 12 distinct values among the remaining observations. Step 6: Total distinct values = 1 (for 28) + 1 (for 35) + 12 (for the rest) = 14.

Question 20

Five numbers have a mean of 32. When a sixth number is added, the mean becomes 30. What is the sixth number?

Accepted Answer

Step 1: Sum of 5 numbers = 5 × 32 = 160. Step 2: Sum of 6 numbers = 6 × 30 = 180. Step 3: Sixth number = 180 − 160 = 20.

IBPS Clerk Statistics Questions

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