Question

The average marks of 12 students is 68. If the marks of one student are excluded, the average becomes 66. The excluded student’s marks are:

• A. 84
• B. 88
• C. 90
• D. 92

Hint:

Use the deviation method to find the answer in seconds! The average dropped from $68$ to $66$, which is a decrease of $-2$ marks for each of the remaining $11$ students. This means the excluded student took away an extra $11 \times 2 = 22$ marks above the old average. $$\text{Excluded Marks} = \text{Old Average} + \text{Total Deficit} = 68 + 22 = 90$$ This saves you from doing long multiplications completely!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
An average value represents the sum of all numerical entries divided by the total count of elements in a given set. When an individual score is excluded from a dataset, both the overall sum and the total number of individuals decrease. We can identify the specific value of the excluded item by calculating the difference between the initial total sum and the new total sum.

Step 2: Key Formula or Approach:
1. $\text{Total Sum} = \text{Average} \times \text{Number of Observations}$
2. $\text{Excluded Value} = \text{Initial Total Sum} - \text{New Total Sum}$

Step 3: Detailed Explanation:
Let's calculate the total values before and after the exclusion step: Initial State: There are $12$ students with an average score of $68$. $$\text{Initial Total Sum} = 12 \times 68 = 816$$ New State: One student's marks are excluded, so the number of remaining students becomes $12 - 1 = 11$. Their updated collective average drops to $66$. $$\text{New Total Sum} = 11 \times 66 = 726$$ Finding the Excluded Marks: Subtract the new total sum from our initial total sum to find the specific marks belonging to the excluded student: $$\text{Excluded Student's Marks} = 816 - 726 = 90$$

Step 4: Final Answer:
The excluded student's marks are 90.