A 100 mark examination was administered to a class of 50 students. Despite only integer marks being given, the average score of the class was 47.5. Then, the maximum number of students who could get marks more than the class average is

To find the maximum number of students who could have marks greater than the class average, we start by analyzing the given information:

- The total number of students is \(50\).
- The average score is \(47.5\).
- The sum of all scores is \(47.5 \times 50 = 2375\).

Since the average is \(47.5\) and marks are integers, not all students can have the average mark. To maximize the number of students with marks above the average, we want as many students as possible to have marks below or equal to the average.

### Steps to Solve:

1. **Determine Minimum Scores Below Average**: Since \(47.5\) is not an integer, we consider scores of 47 or lower to be below the average.

2. **Assign Marks to Maximize Above-Average Students**:
    - Assume the number of students scoring 47 or less is \(n\).
    - The total score contribution from these \(n\) students must be \(47 \times n\) or less.

3. **Remaining Students**: Let the remaining students, \(50 - n\), score above the average.

4. **Equation Setup**: 
   - Total score sum: \(47n + x(50 - n) = 2375\), where \(x\) is the minimum score for above-average students, starting from 48.
   - Simplify: \((50 - n)x = 2375 - 47n\).

To maximize the number \(50 - n\), minimize \(n\). Set the score of below-average students as close as possible to the average:

### Calculation:
- Start with \(n = 25\) (half the students):
  - Score contribution: \(47 \times 25 = 1175\).
  - Required score from remaining 25: \(2375 - 1175 = 1200\).
  - Average for remaining 25: \( \frac{1200}{25} = 48\), which satisfies the above-average condition.

Therefore, the maximum number of students scoring above the average is:

\[
\boxed{25}
\]

Would you like more details or have any questions? Here are some related questions:

1. How does changing the average affect the maximum number of students scoring above average?
2. If the average was a whole number, how would that change the problem?
3. What if scores could be non-integers, how would it impact the calculations?
4. How can you calculate this scenario if the class size changes?
5. Can you find the minimum number of students scoring above average?

**Tip:** Always check if constraints (like integer scores) impact average-based calculations!

Find out how to calculate the maximum number of students scoring above the average in a 100 mark exam with integer marks. This step-by-step guide explains the concepts of average calculation and score optimization. Suitable for high school students in Grades 9-12.

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