The average marks of 10 students in an examination was 25. It was later found that the marks of one student had been wrongly entered as 34 instead of 43. What is the correct average marks of the 10 students?

Introduction / Context:
This question requires you to correct an average when one mark has been entered lower than it should have been. The recorded average of 25 is therefore too small, and we must adjust the total marks to reflect the correct value and then find the updated average.

Given Data / Assumptions:

• Number of students = 10.
• Reported average marks = 25.
• One student's marks were entered as 34 instead of the correct value 43.
• We must compute the correct average marks for the 10 students.

Concept / Approach:
The reported average is based on an incorrect total. We find this total by multiplying 25 by 10. Because the correct value 43 is greater than 34, the true total must be increased by the difference. Once we have the corrected total, we divide by 10 again to obtain the corrected average. This approach is standard for all average correction problems.

Step-by-Step Solution:
Step 1: Incorrect total marks = reported average * number of students = 25 * 10 = 250. Step 2: Wrong value used = 34; correct value = 43. Step 3: Difference between correct and wrong values = 43 - 34 = 9. Step 4: Corrected total marks = 250 + 9 = 259. Step 5: Correct average marks = 259 / 10 = 25.9.

Verification / Alternative check:
Instead of recomputing everything, we can also reason that adding 9 marks to the total and distributing across 10 students will increase the mean by 9 / 10 = 0.9. Therefore the corrected average should be 25 + 0.9 = 25.9, which matches our explicit calculation. This quick check confirms that the corrected average is correct.

Why Other Options Are Wrong:
Option 25.5 would correspond to an increase of only 0.5 in the average, which implies adding 5 marks to the total, not 9. Option 24.1 and option 24.5 are lower than the original average and go in the wrong direction, since the correction increases one mark. Only 25.9 correctly captures the effect of adding 9 marks to the total and dividing by 10.

Common Pitfalls:
A common error is to subtract instead of add the difference between the correct and incorrect values, or to divide the difference by the wrong number of students. Another pitfall is forgetting to update the total explicitly and trying to guess the change in average. Always adjust the total logically and then divide by the full class size.

Final Answer:
The correct average marks of the 10 students is 25.9.