The average marks of 40 students in an examination was 25. Later it was found that one student's marks had been wrongly entered as 73 instead of 37. What is the correct average mark of the 40 students after rectifying the mistake?

Introduction / Context:
This is another example of correcting an average after discovering a data entry error. The mean mark of 40 students is initially calculated using a wrong value of 73 instead of the correct 37. We must adjust the total and recompute the average to find the correct mean for the class.

Given Data / Assumptions:

• Number of students = 40.
• Initial (incorrect) average marks = 25.
• One mark was wrongly entered as 73.
• The correct mark for that student is 37.
• We need to find the corrected average for all 40 students.

Concept / Approach:
Again, we use: average = total marks / number of students. We find the incorrect total with the wrong mark, then adjust it by removing the extra amount introduced by the error and finally divide by 40 to get the corrected average. The extra amount is simply the difference between the wrong mark and the correct mark.

Step-by-Step Solution:
Step 1: Compute incorrect total marks. Incorrect total = 40 * 25 = 1000. Step 2: Identify the error contribution. Wrongly entered mark = 73; correct mark = 37. Error = 73 − 37 = 36 extra marks included. Step 3: Correct the total marks. Correct total = incorrect total − extra = 1000 − 36 = 964. Step 4: Compute the corrected average. Correct average = 964 / 40. Step 5: Divide: 40 * 24 = 960, remainder = 4. So 964 / 40 = 24 + 4/40 = 24.1.
Verification / Alternative check:
The original average 25 will drop because one mark has been lowered from 73 to 37. Average decrease = 36 / 40 = 0.9. So corrected average = 25 − 0.9 = 24.1, confirming our calculation.
Why Other Options Are Wrong:
24.3, 24.5, 24.7 and 24.9 produce totals that are different from 964 when multiplied by 40. For example, if the correct average were 24.5, total would be 24.5 * 40 = 980, which does not match 964.
Common Pitfalls:
Some learners may mistakenly add 36 instead of subtracting, thinking they must 'correct' upwards instead of downwards. Others divide the error 36 by 39 or 41 instead of 40 when attempting to adjust the average, which leads to incorrect results.
Final Answer:
The corrected average marks of the 40 students is 24.1.