Question 1

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 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 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 6

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 7

In a class of 30 students, the mean score is 75. In another class of 20 students, the mean score is 85. What is the combined mean score of all 50 students?

Accepted Answer

Step 1: Total score of first class = 30 × 75 = 2250. Step 2: Total score of second class = 20 × 85 = 1700. Step 3: Combined total score = 2250 + 1700 = 3950. Step 4: Combined mean = 3950 ÷ 50 = 79.

Question 8

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 9

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 10

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.

Question 11

A dataset consists of 7 numbers: 12, 15, 18, 20, 22, 25, 28. If 20 is removed and replaced with 35, what is the change in the median?

Accepted Answer

Step 1: Original dataset in order: 12, 15, 18, 20, 22, 25, 28. For 7 numbers, median position = (7+1)/2 = 4th value. Original median = 20. Step 2: New dataset: 12, 15, 18, 22, 25, 28, 35. Arranging in order: 12, 15, 18, 22, 25, 28, 35. The 4th value = 22. New median = 22. Step 3: Change in median = 22 − 20 = 2.

Question 12

A dataset has 20 observations with mean 25. Another dataset has 30 observations with mean 35. When both datasets are combined, what is the mean of the combined dataset?

Accepted Answer

Step 1: Sum of first dataset = 25 × 20 = 500. Step 2: Sum of second dataset = 35 × 30 = 1050. Step 3: Combined sum = 500 + 1050 = 1550. Step 4: Combined count = 20 + 30 = 50. Step 5: Combined mean = 1550 ÷ 50 = 31. Therefore, the combined mean is 31.

Question 13

A dataset has 11 observations. When arranged in order, the median is 18. The mode is 18 (appearing 3 times). If the mean is 20, what is the sum of all 11 observations?

Accepted Answer

Step 1: The mean is defined as Sum ÷ Number of observations. Step 2: Given: Mean = 20 and n = 11. Step 3: Sum = Mean × n = 20 × 11 = 220. Therefore, the sum of all 11 observations is 220.

Question 14

In a dataset of 9 numbers arranged in ascending order, the median is 15. If the 5th number is 15 and the 4th number is 12, what is the sum of the 6th and 8th numbers if their mean is 19?

Accepted Answer

Step 1: In a dataset of 9 numbers, the median is the 5th value = 15 (confirmed). Step 2: The 6th and 8th numbers have a mean of 19, so their sum = 19 × 2 = 38. Step 3: Therefore, the sum of the 6th and 8th numbers is 38.

Question 15

A frequency distribution has 5 classes with frequencies 8, 12, 20, 15, and 5. The midpoints are 10, 20, 30, 40, and 50 respectively. What is the mean of this distribution?

Accepted Answer

Step 1: Calculate Σ(f × x) = (8×10) + (12×20) + (20×30) + (15×40) + (5×50) = 80 + 240 + 600 + 600 + 250 = 1770. Step 2: Calculate Σf = 8 + 12 + 20 + 15 + 5 = 60. Step 3: Mean = Σ(f × x) ÷ Σf = 1770 ÷ 60 = 29.5. Therefore, the mean is 29.5.

IBPS Clerk Mean, Median, Mode

IBPS Clerk Mean, Median, Mode — Past Exam Questions

Mean, Median, Mode— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Mean, Median, Mode