The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean scroe of 80 and the dullest 25% secured a mean score of 31. The mean score of remaining 55% is :

Using weighted average: Total score = 52×100 = 5200. Brightest 20% (20 students) score = 80×20 = 1600. Dullest 25% (25 students) score = 31×25 = 775. Remaining 55% (55 students) score = 5200-1600-775 = 2825. Mean of remaining = 2825/55 = 51.36 ≈ 51.4%. The key insight is balancing the weighted contributions of all subgroups.