The average marks of 10 students in an examination was calculated as 25. Later, it was found that the marks of one student had been wrongly entered as 34 instead of 43. What is the correct average of the marks of the 10 students after this correction?

Introduction / Context:
This problem focuses on correcting an average after discovering a data entry error. It is a common exam style question where a single wrong entry needs to be fixed and the new average recalculated correctly.

Given Data / Assumptions:
• Number of students = 10.• Initially calculated average marks = 25.• One student's marks were recorded as 34.• The correct marks of that student are 43.• All other marks are assumed correct.

Concept / Approach:
The average marks are the total of all marks divided by the number of students. If one mark is incorrect, we need to correct the total sum. This is done by subtracting the wrong value and adding the correct one. Then we divide by the same number of students to obtain the corrected average.

Step-by-Step Solution:
Step 1: Let S be the total marks based on the incorrect data.Step 2: Since the initial average is 25, S = 10 * 25 = 250.Step 3: Incorrect marks used = 34, correct marks = 43.Step 4: Correct total = S - incorrect value + correct value = 250 - 34 + 43.Step 5: Compute 250 - 34 = 216, then 216 + 43 = 259.Step 6: Correct average = corrected total / number of students = 259 / 10.Step 7: 259 / 10 = 25.9.

Verification / Alternative check:
The difference between the correct and incorrect marks is 43 - 34 = 9. Hence, the correct total marks should be 9 more than the original total. Therefore, the average should increase by 9 / 10 = 0.9 marks. Starting from the original average of 25, we get 25 + 0.9 = 25.9, which supports our detailed calculation.

Why Other Options Are Wrong:
25.5: This assumes an increase of only 0.5 marks in the average, not supported by the 9 mark difference.24.1 and 24.5: These are lower than the original average, while the correction actually increases the total and the mean.

Common Pitfalls:
Students may forget that the total must be adjusted by the full difference between the correct and incorrect values. Another mistake is to change the number of students, which remains the same. Always recompute the total properly and divide by the unchanged count of observations.

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