Correcting class average after two marking errors: The average marks of 30 students are 45. After rechecking, one student gains 45 more marks and another loses 15 marks. What is the adjusted class average?

Introduction / Context:
Error correction in a dataset changes the total, which in turn changes the average. Here two opposite corrections occur, and their net effect adjusts the mean for the same class size.

Given Data / Assumptions:

• n = 30 students; initial average = 45
• Corrections: +45 to one student, −15 to another

Concept / Approach:
Adjusted total = original total + net change. Adjusted average = adjusted total / n. Net change is (+45) + (−15) = +30.

Step-by-Step Solution:
Original total = 30 * 45 = 1350Adjusted total = 1350 + 30 = 1380Adjusted average = 1380 / 30 = 46

Verification / Alternative check:
Average increases by net change / n = 30 / 30 = 1, so 45 + 1 = 46, confirming the result.

Why Other Options Are Wrong:
45 ignores the net increase; 44 decreases incorrectly; 47 and 46.5 overstate the impact of the +30 net correction.

Common Pitfalls:
Adding absolute changes without considering their signs or re-dividing by a wrong class size.

Final Answer:
46