The Highest Possible Marks: Decoding Student Performance Based on Average Scores

Understanding how to calculate the highest possible marks based on an average score can help in comprehending student performance effectively. In the given scenario, we explore how to determine the highest possible mark for 10 students when their average score is known and all students scored above a certain threshold. This article delves into the mathematical calculations and logical reasoning required to find the solution.

Scenario and Calculation

The total marks obtained by 10 students is 4700, as their average score is 470. Each student scored more than 468 marks. To explore the highest possible marks, we start by setting a base case and then determine the optimal distribution of marks.

Minimum and Maximum Scores

The minimum possible score for each student is 469, as they all scored above 468.

Let's assume 9 students scored the minimum possible score of 469:

To find the highest possible mark, we subtract the total of these 9 students' scores from the overall total score:

4700 - 4221 479

Optimal Distribution and Highest Score

Given the total score of 4700 and the minimum score of 469, we can calculate the highest possible score for the 10th student. The highest possible score for the 10th student can be determined as follows:

If 9 students scored 469, the remaining score for the 10th student would be:

4700 - (9 x 469) 479

Mathematical Decomposition of The Solution

Starting with the total score of 4700, we distribute the minimum scores to 9 students, each scoring 469. The equation is as follows:

10 x 470 4700

To find the minimum, each student must score at least 469:

9 x 469 4221

The remaining score, which is the highest possible score for the 10th student, is:

4700 - 4221 479

Alternative Approach

Another method involves assuming an average of 468 to derive the maximum score:

The total score if the average were 468 would be:

10 x 468 4680

To increase the average to 470, the total score must be increased by 20:

4700 - 4680 20

If 9 students each score 468, the 10th student must score:

468 20 488

Thus, the highest possible score is 488.

Conclusion

The highest possible score is determined by distributing the minimum scores to nine students, and the remaining score is attributed to the 10th student. In this case, the highest possible score is 479. This method ensures that the average score is maintained and maximizes the score for one student under the given conditions.