Some students of a class appeared in an examination. Their average score remained 52. If the average score of the top 20% of them was 80 and that of the bottom 20% was 30, then find the average score of the remaining students.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 50
Total score \(=\) average \(\times\) number of students, so the score of the middle group is the total score of the class minus the scores of the top and bottom groups.
Assuming the class to have 100 students:
Total score of the class \(=100\times52=5200\)
Top 20 students: \(20\times80=1600\)
Bottom 20 students: \(20\times30=600\)
Remaining 60 students: \(5200-1600-600=3000\)
Their average \(\displaystyle =\frac{3000}{60}=50\)