The average marks in Science for a class of 20 students was calculated as 68. Later it was found that the marks of two students had been misread as 48 and 65 instead of the correct values 72 and 61 respectively. What is the correct average (in marks) after rectifying this mistake?

Introduction / Context:
This question is about correcting an average when some of the data values were recorded incorrectly. The original class average for Science was computed using two misread marks. Once we know both the wrong entries and their correct values, we can adjust the total and find the new, accurate average. This type of question regularly appears in aptitude tests on averages and data correction.

Given Data / Assumptions:

• Number of students in the class = 20.
• Original average marks (with errors) = 68.
• Two marks were recorded as 48 and 65.
• The correct marks for these two students are 72 and 61 respectively.
• We need the corrected average after replacing the wrong values with the correct ones.

Concept / Approach:
Average is defined as total marks divided by number of students. When we discover that some marks are incorrect, we do not recompute everything from scratch. Instead, we adjust the incorrect total by subtracting the misread marks and adding the correct marks. The new average is the corrected total divided by the same number of students. This method is efficient and avoids reprocessing all individual marks.

Step-by-Step Solution:
Step 1: Compute the original total marks based on the incorrect average. Original total = number of students * original average. Original total = 20 * 68 = 1360. Step 2: Find how much the two incorrect entries differ from the correct values. Wrong marks were 48 and 65. Correct marks are 72 and 61. Total wrong contribution = 48 + 65 = 113. Total correct contribution = 72 + 61 = 133. Step 3: Adjust the total marks. Corrected total = original total − wrong contribution + correct contribution. Corrected total = 1360 − 113 + 133. Compute 1360 − 113 = 1247; then 1247 + 133 = 1380. Step 4: Compute the corrected average. Correct average = corrected total / number of students = 1380 / 20. 1380 / 20 = 69.
Verification / Alternative check:
Notice that the net increase to the total from the correction is 133 − 113 = 20. Since there are 20 students, adding 20 marks in total increases the class average by 20 / 20 = 1 mark. Original average was 68, so new average must be 68 + 1 = 69, confirming the calculation.
Why Other Options Are Wrong:
Options 68.5 and 69.5 suggest a half mark change which would require a total change of 10 marks, not 20, which does not fit the data. An average of 70 would require an even larger increase to the total marks. An average of 67.5 would imply a decrease, which contradicts the fact that the correct marks are higher overall than the misread marks.
Common Pitfalls:
A common error is to simply replace the wrong marks with the correct ones without adjusting the total used for the original average. Another mistake is miscomputing the difference between the wrong and correct marks, which directly affects the new average.
Final Answer:
The correct average marks of the class is 69.