Question 1

The mean of five numbers is 18. Four of the numbers are 14, 16, 20, and 22. What is the fifth number?

Accepted Answer

Step 1: Sum of five numbers = Mean × Count = 18 × 5 = 90. Step 2: Sum of four known numbers = 14 + 16 + 20 + 22 = 72. Step 3: Fifth number = 90 - 72 = 18.

Question 2

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 3

A teacher records the test scores of 6 students: 45, 52, 48, 52, 55, 48. What is the median score?

Accepted Answer

Step 1: Arrange data in ascending order: 45, 48, 48, 52, 52, 55. Step 2: Count observations: n = 6 (even). Step 3: For even n, median = (value at position n/2 + value at position (n/2)+1) ÷ 2 = (value at 3rd position + value at 4th position) ÷ 2 = (48 + 52) ÷ 2 = 100 ÷ 2 = 50.

Question 4

The mean of 8 numbers is 24. If one number is removed, the mean of the remaining 7 numbers becomes 22. What is 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 5

The ages of 6 people are: 22, 25, 28, 30, 35, and 40 years. What is the median age?

Accepted Answer

Step 1: The data is already in ascending order: 22, 25, 28, 30, 35, 40. Step 2: Since there are 6 values (even count), median = (value at position 3 + value at position 4) ÷ 2 = (28 + 30) ÷ 2 = 58 ÷ 2 = 29. Therefore, the median age is 29 years.

Question 6

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: 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, median = 28.

Question 7

A dataset has 5 values: 10, 15, 20, 25, 30. If each value is increased by 5, what is the new mean?

Accepted Answer

Step 1: Original mean = (10 + 15 + 20 + 25 + 30) ÷ 5 = 100 ÷ 5 = 20. Step 2: When each value is increased by 5, the mean also increases by 5. Step 3: New mean = 20 + 5 = 25. Alternatively: New sum = (10+5) + (15+5) + (20+5) + (25+5) + (30+5) = 15 + 20 + 25 + 30 + 35 = 125. New mean = 125 ÷ 5 = 25.

Question 8

The following data represents the number of books read by students: 3, 5, 7, 5, 9, 5, 11. What is the mode?

Accepted Answer

Step 1: List all values: 3, 5, 7, 5, 9, 5, 11. Step 2: Count frequency of each value: 3 appears 1 time, 5 appears 3 times, 7 appears 1 time, 9 appears 1 time, 11 appears 1 time. Step 3: The value with highest frequency is 5 (appears 3 times). Therefore, mode = 5.

Question 9

A dataset has 7 observations: 10, 15, 20, 25, 30, 35, 40. If one more observation of value 25 is added, how does the median change?

Accepted Answer

Step 1: Original dataset (7 values): 10, 15, 20, 25, 30, 35, 40. Median = 4th value = 25. Step 2: New dataset (8 values): 10, 15, 20, 25, 25, 30, 35, 40. Median = (4th + 5th values) ÷ 2 = (25 + 25) ÷ 2 = 25. Step 3: The median remains 25 (no change).

Question 10

The mean of 4 numbers is 25. If three of the numbers are 20, 24, and 26, what is the fourth number?

Accepted Answer

Step 1: Mean = 25 and number of observations = 4. Step 2: Sum of all 4 numbers = Mean × Count = 25 × 4 = 100. Step 3: Sum of three known numbers = 20 + 24 + 26 = 70. Step 4: Fourth number = Total sum − Sum of three numbers = 100 − 70 = 30.

Question 11

The dataset is: 7, 9, 5, 9, 3, 9, 11. What is the mode of this dataset?

Accepted Answer

Step 1: Count the frequency of each value. 3 appears 1 time, 5 appears 1 time, 7 appears 1 time, 9 appears 3 times, 11 appears 1 time. Step 2: The value with highest frequency is 9 (appears 3 times). Therefore, the mode is 9.

Question 12

The median of 6 numbers is 15. If the numbers in ascending order are: 8, 12, x, 18, 20, 24, what is the value of x?

Accepted Answer

Step 1: For 6 observations (even number), Median = (3rd value + 4th value) ÷ 2. Step 2: The 3rd value is x and the 4th value is 18. Step 3: (x + 18) ÷ 2 = 15. Step 4: x + 18 = 30. Step 5: x = 12.

Question 13

The mean of a dataset is 25. When a number 40 is added, the new mean becomes 26. How many numbers were in the original dataset?

Accepted Answer

Step 1: Let the original count be n. Original sum = 25n. Step 2: After adding 40, new sum = 25n + 40. Step 3: New mean = (25n + 40) ÷ (n + 1) = 26. Step 4: 25n + 40 = 26(n + 1) = 26n + 26. Step 5: 25n + 40 = 26n + 26, so 40 − 26 = 26n − 25n, thus n = 14.

Question 14

In a dataset of 10 numbers, the mode is 8 (appearing 4 times), and the remaining 6 numbers are all distinct and different from 8. If the sum of all 10 numbers is 95, what is the mean?

Accepted Answer

Step 1: The mode 8 appears 4 times, contributing 8 × 4 = 32 to the sum. Step 2: The remaining 6 distinct numbers sum to 95 − 32 = 63. Step 3: Mean = Total sum ÷ Total count = 95 ÷ 10 = 9.5.

Question 15

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 16

A dataset contains 6 numbers: 10, 15, 20, 25, 30, and x. The mean is 22. What is the mode if x = 20?

Accepted Answer

Step 1: Sum of known 5 numbers = 10 + 15 + 20 + 25 + 30 = 100. Step 2: Sum of all 6 numbers = 22 × 6 = 132. Step 3: x = 132 − 100 = 32. Step 4: But we're told x = 20, so the dataset is {10, 15, 20, 20, 25, 30}. Step 5: The mode is the value appearing most frequently = 20 (appears twice).

Question 17

A dataset has 12 values. The mean is 20. If three values (18, 22, 20) are removed, what is the mean of the remaining 9 values?

Accepted Answer

Step 1: Sum of all 12 values = 12 × 20 = 240. Step 2: Sum of removed values = 18 + 22 + 20 = 60. Step 3: Sum of remaining 9 values = 240 − 60 = 180. Step 4: Mean of remaining 9 values = 180 ÷ 9 = 20.

Question 18

A dataset has 5 numbers with mean 20. Two numbers are 18 and 22. The remaining three numbers are in the ratio 2:3:5. What is the median of this dataset?

Accepted Answer

Step 1: Sum of all 5 numbers = 20 × 5 = 100. Step 2: Sum of remaining 3 numbers = 100 − 18 − 22 = 60. Step 3: If the three numbers are 2x, 3x, 5x, then 2x + 3x + 5x = 60, so 10x = 60, x = 6. The three numbers are 12, 18, 30. Step 4: Ordered dataset = {12, 18, 18, 22, 30}. Step 5: Median (middle value of 5) = 18.

Question 19

The median of five consecutive odd numbers is 15. What is the sum of the largest and smallest numbers in this set?

Accepted Answer

Step 1: If the median of 5 consecutive odd numbers is 15, then 15 is the middle (3rd) number. Step 2: The five numbers are: 11, 13, 15, 17, 19. Step 3: Smallest = 11, Largest = 19. Step 4: Sum = 11 + 19 = 30.

Question 20

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

Accepted Answer

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

Question 21

The median of the dataset {12, 18, 24, 30, 36} is found. If a new number 28 is added to this dataset, what is the new median?

Accepted Answer

Step 1: Original dataset has 5 numbers (odd), so median is the 3rd value = 24. Step 2: After adding 28, the ordered dataset becomes {12, 18, 24, 28, 30, 36} with 6 numbers (even). Step 3: New median = (24 + 28) ÷ 2 = 52 ÷ 2 = 26.

Question 22

In a dataset of 10 numbers, the mode is 15 (appearing 4 times), and the remaining 6 numbers are all distinct and different from 15. If the sum of all 10 numbers is 140, what is the mean?

Accepted Answer

Step 1: The mode (15) appears 4 times, contributing 15 × 4 = 60 to the sum. Step 2: The remaining 6 distinct numbers sum to 140 − 60 = 80. Step 3: Mean = Total sum ÷ Count = 140 ÷ 10 = 14.

Question 23

A dataset has 5 numbers with mean 32 and median 30. If the numbers in ascending order are a, b, 30, d, e, and a + b = 48, what is the value of d + e?

Accepted Answer

Step 1: Mean = 32, so sum of all 5 numbers = 5 × 32 = 160. Step 2: The median is 30 (the 3rd number). Step 3: Sum = a + b + 30 + d + e = 160. Step 4: Given a + b = 48, substitute: 48 + 30 + d + e = 160. Step 5: d + e = 160 − 48 − 30 = 82.

Question 24

In a dataset of 10 numbers, the median is 15. When a new number 25 is added, the median of the 11 numbers becomes 16. Which of the following could be true about the original dataset?

Accepted Answer

Step 1: With 10 numbers, median is the average of 5th and 6th values when sorted: (5th + 6th)/2 = 15, so 5th + 6th = 30. Step 2: With 11 numbers, median is the 6th value: 6th value = 16. Step 3: Since 25 is added and new median (6th position) = 16, the original 6th value must have shifted. The new 6th value is 16, meaning at least 5 values are ≤16 in the new dataset. Step 4: Original 5th value ≤ 15 and original 6th value ≥ 15 (since their average is 15). For new median to be 16, original 6th value must be ≥ 16. Step 5: If original 6th = 16, then original 5th = 30 − 16 = 14. This satisfies all conditions.

SSC CHSL Mean, Median, Mode

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