A group of 12 students appeared for a physics test. The average of the top 6 scores was 84.5, and the average of the bottom 6 scores was 72.75. Later, it was found that a decimal error had occurred, and one of the scores from the bottom half was mistakenly recorded as 58.2 instead of 85.2. What is the corrected overall average of the group?
Show answer & explanation
Correct answer: D
Explanation
Given:
Average of the top 6 students = 84.5
Average of the bottom 6 students = 72.75
A score of 85.2 was recorded as 58.2 instead.
Total marks of the top 6 students = 84.5 × 6 = 507
Total marks of the bottom 6 students = 72.75 × 6 = 436.5
Total marks (Incorrect) = 507 + 436.5 = 943.5
Error in marks = 85.2 − 58.2 = 27
Correct total marks = 943.5 + 27 = 970.5
Revised average = 970.5 / 12 = 80.875