Question 1

In a dataset of 8 observations, the mode is 15 and it appears 4 times. Which of the following statements is definitely true?

Accepted Answer

Step 1: The mode is the value that appears most frequently in a dataset. Step 2: If 15 is the mode and appears 4 times, then no other value can appear 4 or more times. Step 3: This means 15 appears more frequently than any other value. Step 4: Therefore, 15 is the most frequently occurring value in the dataset. The correct statement is that 15 appears more frequently than any other value.

Question 2

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

Accepted Answer

Step 1: Arrange the marks in ascending order: 45, 48, 52, 52, 63. Step 2: Since there are 5 values (odd number), the median is the middle value, which is the 3rd value. Step 3: The 3rd value is 52. Therefore, the median is 52.

Question 3

A dataset has 7 values: 12, 15, 18, 20, 20, 25, 30. What is the mode of this dataset?

Accepted Answer

Step 1: Identify the frequency of each value. Step 2: 12 appears 1 time, 15 appears 1 time, 18 appears 1 time, 20 appears 2 times, 25 appears 1 time, 30 appears 1 time. Step 3: The value 20 has the highest frequency (appears 2 times). Step 4: Therefore, the mode is 20.

Question 4

The mean of a dataset is 50 and the sum of all values is 400. How many values are in the dataset?

Accepted Answer

Step 1: Use the formula: Mean = Sum of all values / Number of values. Step 2: 50 = 400 / n, where n is the number of values. Step 3: n = 400 / 50. Step 4: n = 8. Therefore, there are 8 values in the dataset.

Question 5

The mean of 4 numbers is 32. Three of the numbers are 28, 35, and 36. If a fifth number 40 is added to the dataset, what is the new mean?

Accepted Answer

Step 1: Find the sum of the original 4 numbers: Mean = 32, so Sum = 32 × 4 = 128. Step 2: The three given numbers are 28, 35, 36. Their sum = 28 + 35 + 36 = 99. Step 3: The fourth number = 128 - 99 = 29. Step 4: When 40 is added, new sum = 128 + 40 = 168. Step 5: New number of values = 5. Step 6: New mean = 168 / 5 = 33.6. Therefore, the new mean is 33.6.

Question 6

In a dataset of 12 values, the sum is 480. Three new values (20, 25, 30) are added. What is the new mean?

Accepted Answer

Step 1: Original sum = 480. New values sum = 20 + 25 + 30 = 75. Step 2: Total new sum = 480 + 75 = 555. Step 3: New count = 12 + 3 = 15. Step 4: New mean = 555 ÷ 15 = 37.

Question 7

The mean of 8 numbers is 24. If one number is removed, the mean of the remaining 7 numbers becomes 22. What is the value of the number that was removed?

Accepted Answer

Step 1: Sum of 8 numbers = Mean × Count = 24 × 8 = 192. Step 2: Sum of remaining 7 numbers = 22 × 7 = 154. Step 3: Removed number = 192 − 154 = 38.

Question 8

Five students scored: 45, 52, 48, 55, and 50 marks. If a sixth student scores 70 marks, by how much does the mean increase?

Accepted Answer

Step 1: Original sum = 45 + 52 + 48 + 55 + 50 = 250. Original mean = 250 ÷ 5 = 50. Step 2: New sum = 250 + 70 = 320. New mean = 320 ÷ 6 = 53⅓. Step 3: Increase = 53⅓ − 50 = 3⅓ marks.

Question 9

A dataset contains 9 values: 12, 15, 18, 12, 20, 12, 25, 18, 30. What is the mode of this dataset?

Accepted Answer

Step 1: Count frequency of each value: 12 appears 3 times, 15 appears 1 time, 18 appears 2 times, 20 appears 1 time, 25 appears 1 time, 30 appears 1 time. Step 2: The value with highest frequency is 12 (appears 3 times). Therefore, mode = 12.

Question 10

The median of 7 numbers arranged in ascending order is 28. If the numbers are: 12, 18, 24, x, 35, 42, 50, what is the value of x?

Accepted Answer

Step 1: For 7 numbers, the median is the 4th number (middle position). Step 2: The 4th position in the sequence 12, 18, 24, x, 35, 42, 50 is x. Step 3: Since median = 28, we have x = 28.

Question 11

A teacher records test scores for 10 students. The mean score is 72. After discovering a marking error, one student's score of 58 is corrected to 68. What is the new mean score?

Accepted Answer

Step 1: Original sum = Mean × Count = 72 × 10 = 720. Step 2: Difference in one score = 68 − 58 = 10. Step 3: New sum = 720 + 10 = 730. Step 4: New mean = 730 ÷ 10 = 73.

Question 12

In a dataset, the mean of 15 numbers is 40. When one number is replaced by 70, the new mean becomes 42. What was the original number that was replaced?

Accepted Answer

Step 1: Original sum = 40 × 15 = 600. Step 2: New sum = 42 × 15 = 630. Step 3: Increase in sum = 630 − 600 = 30. Step 4: This increase equals (New number − Original number) = 70 − Original number = 30. Step 5: Original number = 70 − 30 = 40.

Question 13

In a dataset of 10 observations, the median is 35. When a new observation of value 50 is added, the median of the 11 observations becomes 36. What was the 6th observation (middle value) in the original dataset?

Accepted Answer

Step 1: Original dataset (10 values, sorted): median is average of 5th and 6th values = 35, so (5th + 6th)/2 = 35. Step 2: After adding 50, we have 11 values; median is the 6th value = 36. Step 3: Since 50 is larger than 35, it goes to the right. The new 6th value is the old 6th value. Step 4: Therefore, old 6th value = 36.

Question 14

A frequency distribution has mode 45. The frequencies of classes are: [40–45): 12, [45–50): f, [50–55): 8, [55–60): 5. If the mode lies in the [45–50) class, what is the minimum value of f?

Accepted Answer

Step 1: For mode to lie in [45–50), this class must have the highest frequency. Step 2: The modal class frequency must be greater than both adjacent classes. Step 3: f must be > 12 (left adjacent) and f must be > 8 (right adjacent). Step 4: Minimum f = 13 (smallest integer greater than 12).

Question 15

A dataset of 20 numbers has mean 50. The sum of the 10 smallest numbers is 420. If the median of the entire dataset is 48, what is the sum of the 10 largest numbers?

Accepted Answer

Step 1: Total sum of all 20 numbers = 50 × 20 = 1000. Step 2: Sum of 10 smallest = 420. Step 3: Sum of 10 largest = 1000 − 420 = 580. Step 4: Verify with median: median of 20 numbers = (10th + 11th)/2 = 48, so 10th + 11th = 96. This is consistent with the 10 smallest summing to 420 and 10 largest summing to 580.

Question 16

A dataset contains 8 numbers. Their mean is 24. If three numbers (18, 22, 26) are removed from the dataset, what is the mean of the remaining 5 numbers?

Accepted Answer

Step 1: Sum of all 8 numbers = Mean × Count = 24 × 8 = 192. Step 2: Sum of removed numbers = 18 + 22 + 26 = 66. Step 3: Sum of remaining 5 numbers = 192 − 66 = 126. Step 4: Mean of remaining 5 = 126 ÷ 5 = 25.2.

IBPS RRB PO Mean, Median, Mode

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