The average of the marks of 17 students in an examination was first calculated as 71. Later it was found that one mark had been wrongly entered as 65 instead of 56, and another mark as 24 instead of 50. What is the correct average of the marks?

Introduction / Context:
This is a typical “correction of average” problem in statistics. It shows how an initially computed mean can change when errors in individual data values are detected and corrected. You are given the originally reported average and details of the mistakes, and you must recompute the correct average by adjusting the total appropriately.

Given Data / Assumptions:

Number of students = 17.
Originally calculated average = 71 marks.
One student's mark was entered as 65 instead of the true value 56.
Another student's mark was entered as 24 instead of the true value 50.
All other marks are assumed to have been recorded correctly.
We must find the correct average after adjusting for both errors.

Concept / Approach:
Average = total marks / number of students. First, we calculate the original total marks using the original average and number of students. Then we remove the wrong entries and add the correct ones. This yields the true total marks. Finally, we divide the true total by 17 again to get the corrected average. The key is to adjust the total by the net effect of correcting the two errors.

Step-by-Step Solution:
Step 1: Compute original total marks. Original total = 71 * 17 = 1207. Step 2: Adjust for the first mistake. Wrongly entered as 65 instead of 56, so the recorded total is 9 marks too high. Correcting this reduces the total by 65 - 56 = 9. Step 3: Adjust for the second mistake. Wrongly entered as 24 instead of 50, so the recorded total is 26 marks too low. Correcting this increases the total by 50 - 24 = 26. Step 4: Compute corrected total. Corrected total = 1207 - 9 + 26 = 1207 + 17 = 1224. Step 5: Compute corrected average. Corrected average = 1224 / 17 = 72.

Verification / Alternative Check:
Note that the net adjustment to the total is +17 marks (subtract 9, add 26). Increasing the total by 17 marks over 17 students increases the average by exactly 1 mark. So the corrected average must be 71 + 1 = 72, which matches the detailed calculation. This provides a quick mental check that our result is consistent.

Why Other Options Are Wrong:
70 would imply that the corrected total is less than the original total, which contradicts the net increase of 17 marks after fixing the entries.
71 is the original incorrect average and does not reflect the corrected mark entries.
73 would require a total increase of 34 marks across 17 students, but our corrections only add a net 17 marks.

Common Pitfalls:
Learners sometimes forget to subtract the wrong values before adding the correct ones, or they confuse which wrong entry was too high and which was too low. Others try to re-average only the two corrected marks without considering the total. Remember that the average is based on the total of all observations, so corrections must always be applied to the total sum first.

Final Answer:
The correct average of the marks is 72.