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In a seminar, 18 participants scored an average of 72 on an assessment and the other 12 participants scored an average of 82. What was the average score of all 30 participants?
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Correct answer
B
Weight each group average by its number of participants: (18 × 72 + 12 × 82) / 30 = (1,296 + 984) / 30 = 2,280 / 30 = 76.
The dominant trap is (C) 77, the simple average of 72 and 82; it ignores that more participants (18) sit at the lower 72, pulling the true average below the midpoint of 77. (A) 74 is what you get if you lean too hard toward that larger, lower-scoring group, dropping below the true 76. (D) 78 swaps the weights onto the wrong groups, pairing the 18-count with 82 instead of 72.
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