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 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 3

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 4

The mean of 8 numbers is 24. When two new numbers are added to this set, the mean becomes 26. If one of the two new numbers is 35, what is the other new number?

Accepted Answer

Step 1: Sum of original 8 numbers = 8 × 24 = 192. Step 2: Sum of 10 numbers (after adding two new numbers) = 10 × 26 = 260. Step 3: Sum of the two new numbers = 260 − 192 = 68. Step 4: If one new number is 35, the other = 68 − 35 = 33.

Question 5

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 6

The mean of 9 observations is 36. If one observation of value 18 is removed, what is the new mean of the remaining 8 observations?

Accepted Answer

Step 1: Total sum of 9 observations = Mean × Number = 36 × 9 = 324. Step 2: After removing the observation of 18, new sum = 324 − 18 = 306. Step 3: New mean = 306 ÷ 8 = 38.25. Therefore, the answer is 38.25.

Question 7

A dataset consists of 8 numbers. The mean of the first 5 numbers is 12, and the mean of the last 3 numbers is 18. If the median of all 8 numbers (when arranged in ascending order) is 13.5, find the sum of the 4th and 5th numbers in the sorted dataset.

Accepted Answer

Step 1: Sum of first 5 numbers = 5 × 12 = 60. Step 2: Sum of last 3 numbers = 3 × 18 = 54. Step 3: Total sum of all 8 numbers = 60 + 54 = 114. Step 4: Median of 8 numbers = (4th + 5th number)/2 = 13.5, so 4th + 5th = 27. Step 5: Verify: The 4th and 5th positions in sorted order are the middle two values, and their average being 13.5 is consistent with a median calculation. Therefore, the sum of the 4th and 5th numbers is 27.

Question 8

A dataset consists of 8 numbers. The mean of the first 5 numbers is 12, and the mean of the last 3 numbers is 18. If the median of all 8 numbers (when arranged in ascending order) is 13.5, find the sum of the 4th and 5th numbers in the sorted dataset.

Accepted Answer

Step 1: Sum of first 5 numbers = 5 × 12 = 60. Step 2: Sum of last 3 numbers = 3 × 18 = 54. Step 3: Total sum of all 8 numbers = 60 + 54 = 114. Step 4: Median of 8 numbers = (4th + 5th value)/2 = 13.5, so 4th + 5th = 27. Step 5: Verify: The 4th and 5th positions are the middle values in a sorted 8-element dataset, and their average equals the median. Therefore, the sum of the 4th and 5th numbers is 27.

Question 9

The mean of four numbers is 20. Three of the numbers are 16, 22, and 24. What is the fourth number?

Accepted Answer

Step 1: Use the mean formula: Mean = (Sum of all values) / (Number of values). Step 2: Given Mean = 20 and n = 4. Step 3: Sum of all 4 numbers = 20 × 4 = 80. Step 4: Sum of the three known numbers = 16 + 22 + 24 = 62. Step 5: Fourth number = 80 - 62 = 18. Therefore, the fourth number is 18.

Question 10

The mean of four numbers is 20. Three of the numbers are 16, 18, and 22. What is the fourth number?

Accepted Answer

Step 1: Mean of 4 numbers = 20, so sum of 4 numbers = 4 × 20 = 80. Step 2: Sum of three known numbers = 16 + 18 + 22 = 56. Step 3: Fourth number = 80 − 56 = 24.

Question 11

The mode of the dataset: 12, 15, 12, 18, 12, 20, 15 is ___.

Accepted Answer

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

Question 12

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

Accepted Answer

Step 1: List the data: 45, 52, 48, 52, 63. Step 2: Count frequency of each value — 45 appears 1 time, 52 appears 2 times, 48 appears 1 time, 63 appears 1 time. Step 3: Mode is the value with highest frequency = 52.

Question 13

The mode of the dataset 7, 9, 7, 11, 9, 7, 13 is:

Accepted Answer

Step 1: List the data: 7, 9, 7, 11, 9, 7, 13. Step 2: Count frequency — 7 appears 3 times, 9 appears 2 times, 11 appears 1 time, 13 appears 1 time. Step 3: Mode is the value with the highest frequency = 7 (appears 3 times).

Question 14

The marks obtained by 5 students in a test are: 12, 18, 15, 12, and 23. What is the mean of their marks?

Accepted Answer

Step 1: Sum of all marks = 12 + 18 + 15 + 12 + 23 = 80. Step 2: Number of students = 5. Step 3: Mean = Sum ÷ Number of observations = 80 ÷ 5 = 16.

Question 15

The dataset is: 7, 9, 7, 11, 7, 13, 15. What is the mode of this dataset?

Accepted Answer

Step 1: List the frequency of each value: 7 appears 3 times, 9 appears 1 time, 11 appears 1 time, 13 appears 1 time, 15 appears 1 time. Step 2: The mode is the value that appears most frequently. Step 3: 7 appears 3 times, which is the highest frequency. Therefore, mode = 7.

Question 16

The heights (in cm) of 7 children are arranged in ascending order as: 120, 125, 128, 132, 135, 140, 145. What is the median height?

Accepted Answer

Step 1: The dataset has 7 observations (odd number). Step 2: For an odd number of observations, the median is the middle value. Step 3: The middle position = (7 + 1) ÷ 2 = 4th position. Step 4: The 4th value in the ordered list is 132. Therefore, median = 132 cm.

Question 17

The mean of 8 observations is 15. If two observations are 10 and 12, what is the sum of the remaining 6 observations?

Accepted Answer

Step 1: Sum of all 8 observations = Mean × Number of observations = 15 × 8 = 120. Step 2: Sum of the two given observations = 10 + 12 = 22. Step 3: Sum of remaining 6 observations = Total sum − Sum of two observations = 120 − 22 = 98. Therefore, the sum of the remaining 6 observations is 98.

Question 18

A dataset contains 8 values: 10, 14, 18, 22, 26, 30, 34, 38. What is the median?

Accepted Answer

Step 1: The dataset has 8 observations (even number). Step 2: For an even number of observations, the median is the average of the two middle values. Step 3: The two middle positions are (8 ÷ 2) = 4th and 5th. Step 4: The 4th value is 22 and the 5th value is 26. Step 5: Median = (22 + 26) ÷ 2 = 48 ÷ 2 = 24.

Question 19

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

Accepted Answer

Step 1: Arrange the data: 45, 48, 52, 52, 63. Step 2: Identify the frequency of each value. The value 52 appears twice, while all others appear once. Step 3: Mode is the value with the highest frequency. Therefore, mode = 52.

Question 20

The ages of 7 people are: 22, 25, 28, 30, 32, 35, 40. What is the median age?

Accepted Answer

Step 1: Count the values: n = 7 (odd number). Step 2: The data is already in ascending order. Step 3: For odd n, median position = (n+1)/2 = (7+1)/2 = 4. Step 4: The 4th value in the ordered list is 30. Therefore, median age = 30.

Question 21

The mean of 6 numbers is 24. If one number is replaced by 36, the new mean becomes 26. What was the original number that was replaced?

Accepted Answer

Step 1: Sum of original 6 numbers = Mean × Count = 24 × 6 = 144. Step 2: Sum of new 6 numbers = New Mean × Count = 26 × 6 = 156. Step 3: Difference in sum = 156 − 144 = 12. Step 4: This difference equals (New number − Original number), so 36 − Original = 12. Step 5: Original number = 36 − 12 = 24. Therefore, the original number was 24.

Question 22

The mean of six numbers is 15. If five of the numbers are 10, 12, 14, 18, and 20, what is the sixth number?

Accepted Answer

Step 1: Use the formula: Mean = (Sum of all values) / (Number of values). Step 2: Given Mean = 15 and n = 6. Step 3: Sum of all 6 numbers = 15 × 6 = 90. Step 4: Sum of the five known numbers = 10 + 12 + 14 + 18 + 20 = 74. Step 5: Sixth number = 90 - 74 = 16. Therefore, the sixth number is 16.

Question 23

The median of the dataset {12, 18, 24, 30, 36} is ___.

Accepted Answer

Step 1: Count the number of values: n = 5 (odd number). Step 2: For an odd number of values, the median is the middle value when arranged in order. Step 3: The dataset is already in ascending order. The middle position is (5+1)/2 = 3rd position. Step 4: The 3rd value is 24. Therefore, median = 24.

Question 24

The median of the dataset 5, 8, 12, 15, 20, 25 is:

Accepted Answer

Step 1: Count the data points: 6 values (even number). Step 2: For even number of values, median is the average of the two middle values. Step 3: The data is already sorted: 5, 8, 12, 15, 20, 25. Step 4: The two middle values are at positions 3 and 4: 12 and 15. Step 5: Median = (12 + 15)/2 = 27/2 = 13.5.

Question 25

The median of the dataset 12, 18, 24, 30, 36 is:

Accepted Answer

Step 1: Count the data points: 5 values (odd number). Step 2: For odd number of values, median is the middle value when arranged in order. Step 3: The data is already sorted: 12, 18, 24, 30, 36. Step 4: Middle position = (5+1)/2 = 3rd value = 24.

Question 26

A dataset has 8 values: 5, 8, 10, 12, 15, 18, 20, 25. What is the median?

Accepted Answer

Step 1: Count the values: n = 8 (even number). Step 2: The data is already in ascending order. Step 3: For even n, the median is the average of the two middle values at positions n/2 and (n/2 + 1). Step 4: Positions are 8/2 = 4 and 5. Step 5: The 4th value is 12 and the 5th value is 15. Step 6: Median = (12 + 15) / 2 = 27 / 2 = 13.5. Therefore, median = 13.5.

Question 27

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 28

The mean of 8 numbers is 15. If one number is removed, the mean of the remaining 7 numbers becomes 14. What is the removed number?

Accepted Answer

Step 1: Mean of 8 numbers = 15, so sum of 8 numbers = 8 × 15 = 120. Step 2: Mean of remaining 7 numbers = 14, so sum of 7 numbers = 7 × 14 = 98. Step 3: Removed number = 120 − 98 = 22.

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