Correcting a misrecorded mark in a class mean: The mean marks of 30 students is 58.5. Later, it was found that a mark of 75 had been wrongly recorded as 57. What is the correct mean?

Introduction / Context:
We correct the class total by replacing a misrecorded value, then recompute the mean.

Given Data / Assumptions:

• n = 30
• Original mean = 58.5 → original total = 58.5 * 30
• Recorded 57 should be 75 (increase by 18)

Concept / Approach:
Corrected total = original total + 18. Correct mean = corrected total / 30.

Step-by-Step Solution:
Original total = 58.5 * 30 = 1755Corrected total = 1755 + 18 = 1773Correct mean = 1773 / 30 = 59.1

Verification / Alternative check:
The net increase per student = 18 / 30 = 0.6. 58.5 + 0.6 = 59.1, consistent.

Why Other Options Are Wrong:
57.4, 57.5, 58.1, 58.9 are not the corrected mean after adding 18 to the total.

Common Pitfalls:
Subtracting 18 instead of adding; forgetting to keep the count at 30.

Final Answer:
59.1