In a class of 17 students, the average marks were first calculated as 71, but it was later found that one student's mark had been entered as 65 instead of 56 and another student's mark as 24 instead of 50. After correcting both entries, what is the correct average marks of all 17 students?

Introduction / Context:
This question tests the concept of correcting an average when some of the individual data values were entered incorrectly. Such problems are very common in competitive exams because they mix arithmetic mean, totals, and error analysis in one compact question. Understanding how to update the total when a few marks are wrongly recorded helps you handle many real classroom and survey situations accurately.

Given Data / Assumptions:

• Number of students = 17.
• Originally calculated average marks = 71.
• One mark was entered as 65 instead of 56.
• Another mark was entered as 24 instead of 50.
• We assume all other marks are correct.

Concept / Approach:
The key idea is that average = total sum / number of observations. If some values are wrong, the original total is also wrong. To correct the average, we first compute the old total using the wrong average, then remove the wrong entries, add the correct ones, and finally divide the new total by the same number of students to get the corrected average.

Step-by-Step Solution:
Step 1: Original total marks (with mistakes) = 71 * 17.Step 2: 71 * 17 = 1207, so original total = 1207.Step 3: Replace 65 with 56 and 24 with 50. Net correction = (56 - 65) + (50 - 24).Step 4: (56 - 65) = -9 and (50 - 24) = 26. Net correction = -9 + 26 = 17.Step 5: Correct total marks = 1207 + 17 = 1224.Step 6: Correct average = 1224 / 17 = 72.

Verification / Alternative check:
Another way is to think directly in terms of totals. If two entries are adjusted by a net increase of 17 marks, the average increase per student must be 17 / 17 = 1 mark. Since the original average was 71, the new average becomes 71 + 1 = 72. This matches our previous calculation, so the result is consistent.

Why Other Options Are Wrong:
Option 70 would correspond to a net negative correction, which contradicts the given changes. Option 71 would mean no overall correction, which is not possible because the two corrections do not cancel each other. Option 73 would require a larger positive change in the total than what actually occurs. Option 69 is even further away and does not align with any reasonable miscalculation of the corrections.

Common Pitfalls:

• Forgetting to multiply average by the number of students to get the total.
• Mixing up which mark is the correct one and which mark is the wrong one.
• Adding both differences instead of considering the correct sign (one change reduces the total, the other increases it).

Final Answer:
The corrected average marks of the 17 students is 72.