The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are

Correct Option (B)

The initial total marks for 100 students, with an average of 40, were calculated as 100 × 40 = 4000. It was subsequently identified that a student's marks of 53 were erroneously recorded as 83. To correct the total, the difference between the misread value and the actual value (83 - 53 = 30) must be subtracted from the initial total. Thus, the corrected total marks are 4000 - 30 = 3970. The corrected mean marks are then calculated by dividing the corrected total marks by the number of students: 3970 / 100 = 39.7.

Incorrect Options:

• Option (A) 39: This value would imply a total sum of 3900 (39 × 100), which represents a larger reduction in total marks than the actual correction of 30 marks.
• Option (C) 40: This value represents the original, uncorrected mean. It would be correct only if the identified error had no net impact on the total sum, which is not the case here.
• Option (D) 40.3: This value would imply a total sum of 4030 (40.3 × 100), which suggests an increase in the total marks, contrary to the required correction.