The average marks of 45 students was initially shown as 65, but one entry was wrongly recorded as 84 instead of 48. What is the correct average of the 45 students after rectifying this mistake?

Introduction / Context:
This question is about correcting an average when one of the data values has been misrecorded. We are given the original average based on an incorrect value and then told what the value should have been. The task is to adjust the total marks accordingly and recompute the true average. This type of problem appears frequently in aptitude tests to check clarity on how averages relate to total sums.

Given Data / Assumptions:
- Number of students = 45
- Incorrect average shown = 65 marks
- One student's mark was recorded as 84 instead of the correct value 48
- All other entries are correct
- We need the corrected average of the same 45 students

Concept / Approach:
The average of a set of numbers is total sum divided by the number of observations. If one item is wrong, the initial total sum is also wrong. We first reconstruct the wrong total by multiplying the reported average by the number of students. Then we remove the wrong entry and add the correct one to obtain the corrected total. Dividing this corrected total by the same number of students gives the true average.

Step-by-Step Solution:
Step 1: Compute the total marks based on the wrong average: wrong total = 65 × 45 = 2925 marks.Step 2: The wrong entry is 84, but the correct entry should be 48. So we must subtract 84 and then add 48.Step 3: Correct total = 2925 − 84 + 48 = 2925 − 36 = 2889 marks.Step 4: Correct average = 2889 ÷ 45 = 64.2 marks.Step 5: Therefore, the accurate class average after correction is 64.2 marks.

Verification / Alternative check:
The change in the total marks is simply the difference between the wrong and correct entries: 84 − 48 = 36 marks extra were counted. Dividing this extra 36 marks by 45 students gives 36 ÷ 45 = 0.8. So the correct average must be 65 − 0.8 = 64.2, which matches the value obtained by recomputing the total. This cross check confirms that the corrected average is consistent.

Why Other Options Are Wrong:
Values like 65.8 or 67.4 would require an increase in the total marks, but the correction actually reduces the total because 84 is larger than 48. The option 62.6 implies a much larger reduction than the 36 marks difference, and 66.0 also does not match the precise adjustment of 0.8 we computed. Only 64.2 aligns with the corrected total of 2889 marks.

Common Pitfalls:
Learners sometimes subtract the difference 36 directly from the average instead of dividing it by the number of students, which would give 65 − 36 = 29, an impossible result. Another mistake is to use 84 − 48 with the wrong sign, adding 0.8 rather than subtracting it. Always remember that the correction to the average is equal to the net change in total marks divided by the number of observations.

Final Answer:
The correct average marks of the 45 students is 64.2 marks.