The average marks of 18 students in an examination is 60. Later it is found that the marks of one student were wrongly entered as 63 instead of 36. What is the correct class average after the error is rectified?

Introduction / Context:
This problem illustrates how a single incorrect data entry can change the average and how to correct the average once the mistake is discovered. The marks of one student were entered incorrectly, leading to an overstated class average. After identifying the error, we must recompute the correct average. This type of question is very common in aptitude tests dealing with averages and data correction.

Given Data / Assumptions:
- Number of students = 18.
- Initially calculated average marks = 60.
- Therefore, initial total marks based on the incorrect data = 18 * 60.
- One student marks were wrongly entered as 63 instead of 36.
- We must find the correct average after replacing 63 with 36.

Concept / Approach:
The idea is to first compute the incorrect total marks from the given incorrect average. Then we adjust this total by subtracting the wrong entry and adding the correct mark. After obtaining the corrected total, we divide by the number of students to get the corrected average. This is a simple and reliable correction method for average problems with misentered values.

Step-by-Step Solution:
Step 1: Incorrect total marks based on the wrong data = 18 * 60 = 1080.Step 2: We know that 63 was recorded instead of the true mark 36.Step 3: Difference between wrong and correct mark = 63 - 36 = 27.Step 4: The incorrect total is larger than the true total by 27 marks.Step 5: Correct total marks = 1080 - 27 = 1053.Step 6: Number of students remains 18.Step 7: Correct average = 1053 / 18.Step 8: Compute 1053 / 18. Since 18 * 58 = 1044 and 18 * 0.5 = 9, we have 1044 + 9 = 1053, so the average is 58.5.Step 9: Therefore, the correct class average is 58.5 marks.

Verification / Alternative check:
To verify, imagine the true total is 1053. If one student mark is 36 and the sum of the other 17 students marks is 1053 - 36 = 1017, adding them gives back 1053. Dividing by 18 gives 58.5, so the new average is consistent. Also, the incorrect mark 63 is 27 higher than 36, so using 63 instead of 36 inflated the total by 27 and the average by 27 / 18 = 1.5, which matches the difference between 60 and 58.5.

Why Other Options Are Wrong:
The options 59, 59.5 and 58 do not reflect the exact correction of 27 marks spread over 18 students. Option 60 is simply the original incorrect average and does not incorporate the correction. Only 58.5 matches the corrected total marks and the reduced average after replacing 63 with 36.

Common Pitfalls:
Some students mistakenly add 27 instead of subtracting it from the total, or they divide the difference 27 by the wrong number of students. Others forget that the number of students remains unchanged. To avoid these errors, always identify whether the wrong entry was too high or too low, adjust the total in the correct direction and divide by the correct count of data points.

Final Answer:
The correct average marks of the class is 58.5.