The average marks of 40 students in an examination were calculated as 34. Later, it was discovered that one student's marks had been wrongly entered as 62 instead of the correct value 26. What is the correct average mark of the 40 students?

Introduction / Context:
This is a standard average-correction problem. Initially, the average marks of 40 students were computed using an incorrect data entry. One student's marks were entered as 62 instead of the true value 26. We need to adjust the total and recalculate the correct average for all 40 students.

Given Data / Assumptions:

• Number of students = 40.
• Initial (incorrect) average = 34.
• One wrongly recorded mark = 62 (incorrect), correct mark = 26.
• We must find the corrected average for 40 students.

Concept / Approach:
Average is: average = total marks / number of students. We first compute the incorrect total marks using the given average. Then we correct that total by removing the wrongly added mark and adding the correct one. Finally, we divide the corrected total by 40 to find the corrected average.

Step-by-Step Solution:
Step 1: Compute the incorrect total marks. Incorrect total = 40 * 34 = 1360. Step 2: Identify the error in marks. Incorrect entry = 62, correct value = 26. The error amount = 62 − 26 = 36 (extra marks added). Step 3: Correct the total marks by removing this extra 36. Correct total = incorrect total − 36 = 1360 − 36 = 1324. Step 4: Compute the corrected average. Correct average = 1324 / 40. Step 5: Divide carefully: 40 * 33 = 1320, remainder 4. So 1324 / 40 = 33 + 4/40 = 33.1.
Verification / Alternative check:
Alternatively, note that we reduced the total by 36 marks across 40 students. So the average is reduced by 36 / 40 = 0.9. Incorrect average = 34, new average = 34 − 0.9 = 33.1, confirming the earlier computation.
Why Other Options Are Wrong:
33.3, 33.5 and 33.7 correspond to total marks that differ from 1324 when multiplied by 40. For example, 33.5 * 40 = 1340, which is inconsistent with the corrected total of 1324. 32.9 is smaller than 33.1 and would imply an excessive downward correction.
Common Pitfalls:
A frequent mistake is to add 36 instead of subtracting it, reversing the correction. Another is to divide the error 36 by 39 or another incorrect number instead of by all 40 students when adjusting the average.
Final Answer:
The correct average marks of the 40 students is 33.1.