Question 1

The mode of the following data: 5, 7, 5, 9, 5, 7, 11, 7, 5 is ___.

Accepted Answer

Step 1: Count frequency of each value: 5 appears 4 times, 7 appears 3 times, 9 appears 1 time, 11 appears 1 time. Step 2: Mode is the value with highest frequency = 5 (appears 4 times). Therefore, the mode is 5.

Question 2

If the mean of 6 numbers is 24, what is the sum of all 6 numbers?

Accepted Answer

Step 1: Use the formula: Mean = Sum ÷ Number of observations. Step 2: Rearrange: Sum = Mean × Number of observations. Step 3: Sum = 24 × 6 = 144. Therefore, the sum is 144.

Question 3

The median of 8 numbers arranged in order is the average of the 4th and 5th numbers. If the 4th number is 18 and the 5th number is 22, what is the median?

Accepted Answer

Step 1: For an even number of observations (8), the median is the average of the two middle values. Step 2: The two middle values are the 4th and 5th numbers. Step 3: Median = (18 + 22) ÷ 2 = 40 ÷ 2 = 20. Therefore, the median is 20.

Question 4

A dataset has 5 values. The mean is 16 and four of the values are 12, 14, 18, and 20. What is the fifth value?

Accepted Answer

Step 1: Use Mean = Sum ÷ Count, so Sum = Mean × Count = 16 × 5 = 80. Step 2: Sum of known four values = 12 + 14 + 18 + 20 = 64. Step 3: Fifth value = Total sum − Sum of four values = 80 − 64 = 16. Therefore, the fifth value is 16.

Question 5

The marks obtained by 5 students in a test are: 12, 18, 15, 12, 20. What is the mean of their marks?

Accepted Answer

Step 1: Sum of all marks = 12 + 18 + 15 + 12 + 20 = 77. Step 2: Number of students = 5. Step 3: Mean = 77 ÷ 5 = 15.4. Therefore, the mean is 15.4.

Question 6

The median of the dataset: 8, 14, 6, 10, 12 is ___.

Accepted Answer

Step 1: Arrange data in ascending order: 6, 8, 10, 12, 14. Step 2: Count observations = 5 (odd number). Step 3: Median is the middle value = 3rd value = 10. Therefore, the median is 10.

Question 7

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 8

A dataset has mode 15, which appears 6 times. The dataset also contains the values 10, 12, 15, 15, 15, 15, 15, 15, 18, 20. How many times does the value 20 appear if the mode remains 15 and no other value appears more than 6 times?

Accepted Answer

Step 1: Mode is the most frequently occurring value. Step 2: Value 15 appears 6 times (given in list). Step 3: For 15 to remain the unique mode, no other value can appear 6 or more times. Step 4: Value 20 can appear at most 5 times. Step 5: From the given list, 20 appears once, so it appears 1 time.

Question 9

The mean of a dataset of 12 numbers is 35. After removing two numbers (28 and 42), what is the mean of the remaining 10 numbers?

Accepted Answer

Step 1: Sum of original 12 numbers = 12 × 35 = 420. Step 2: Sum of two removed numbers = 28 + 42 = 70. Step 3: Sum of remaining 10 numbers = 420 − 70 = 350. Step 4: Mean of remaining 10 = 350 ÷ 10 = 35.

Question 10

A class of 20 students has a mean score of 72. Another class of 30 students has a mean score of 78. What is the combined mean score of all 50 students?

Accepted Answer

Step 1: Sum of scores in class 1 = 20 × 72 = 1440. Step 2: Sum of scores in class 2 = 30 × 78 = 2340. Step 3: Total sum = 1440 + 2340 = 3780. Step 4: Combined mean = 3780 ÷ 50 = 75.6.

Question 11

The median of five numbers arranged in ascending order is 18. If the first number is 8 and the last number is 32, and the second number is 14, what is the fourth number if the sum of all five numbers is 90?

Accepted Answer

Step 1: The median of 5 numbers is the 3rd number = 18. Step 2: Numbers are: 8, 14, 18, ?, 32. Step 3: Sum equation: 8 + 14 + 18 + x + 32 = 90. Step 4: 72 + x = 90, so x = 18.

Question 12

In a class of 20 students, the mean score is 75. The mode is 80 (appearing 5 times). If 4 students with score 80 are replaced by 4 students with score 70, what is the new mean? (Assume no other score appears 5 or more times after the change.)

Accepted Answer

Step 1: Original sum = 20 × 75 = 1500. Step 2: We are replacing 4 scores of 80 with 4 scores of 70. Change in sum = 4 × (70 − 80) = 4 × (−10) = −40. Step 3: New sum = 1500 − 40 = 1460. Step 4: New mean = 1460 ÷ 20 = 73.

Question 13

A dataset has 5 numbers with median 18. If the numbers in ascending order are: 12, 15, x, 24, 28, what is the value of x? Additionally, if we add two more numbers (both equal to 18) to make 7 numbers, what is the new median?

Accepted Answer

Step 1: For 5 numbers in ascending order (12, 15, x, 24, 28), median is the 3rd number. So x = 18. Step 2: After adding two 18s, the 7 numbers in order are: 12, 15, 18, 18, 18, 24, 28. Step 3: New median is the 4th number = 18.

Question 14

The mean of 8 numbers is 24. If one number is replaced by 56, the new mean becomes 28. 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 × 28 = 224. Step 3: Difference = 224 − 192 = 32. Step 4: Original number = 56 − 32 = 24.

SSC MTS Mean, Median, Mode

Mean, Median, Mode— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Mean, Median, Mode — Practice Questions

60-Second Revision — Mean, Median, Mode