The average marks of 18 students in an examination was first calculated as 60, but it was later found that one student's marks had been wrongly entered as 63 instead of 36. What is the correct average marks of the class after this correction?

Introduction / Context:
This problem focuses on correcting an average when one of the data values was entered wrongly. Such questions test your understanding of how a single incorrect entry affects the overall mean and how to adjust the total sum and recompute the average once the error is identified.

Given Data / Assumptions:

• Number of students = 18.
• Originally calculated average = 60 marks.
• One student's marks were entered as 63 instead of the correct value 36.
• We need to find the corrected average after replacing 63 with 36.

Concept / Approach:
Average is defined as total sum of observations divided by the number of observations. First, we compute the incorrect total using the wrong average. Then we adjust this total by removing the wrong value and adding the correct one. Finally, we divide the corrected total by the same number of students to obtain the correct average.

Step-by-Step Solution:
Incorrect average = 60 marks. Number of students = 18. Incorrect total marks = 60 * 18 = 1080. Wrong entry used = 63 marks. Correct value should be = 36 marks. Corrected total marks = 1080 - 63 + 36. Corrected total marks = 1080 - 27 = 1053. Correct average = corrected total / number of students. Correct average = 1053 / 18 = 58.5.
Verification / Alternative check:
Difference between wrong and correct marks = 63 - 36 = 27. So the original total was 27 marks too high. Thus, average must decrease by 27 / 18 = 1.5 marks. Original average = 60, so correct average = 60 - 1.5 = 58.5, which matches the earlier result.
Why Other Options Are Wrong:
Option A (59): Assumes a smaller correction than required. Option B (59.5): Does not match the exact decrease needed from the wrong entry. Option C (58): Overshoots the necessary reduction in average. Option D (58.5): Exactly reflects the corrected total and is therefore correct.
Common Pitfalls:
A common mistake is to adjust the average directly without first correcting the total. Some students forget to subtract the wrong entry before adding the correct one, effectively double counting. Another error is to divide the change in marks by the wrong number of students, which gives an incorrect adjustment to the average.
Final Answer:
The correct average marks of the class after correction is 58.5.