A class has two groups: Group A average 90 with 8 students; Group B average 85 with 6 students. What is the overall average score?

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Multiple Choice

A class has two groups: Group A average 90 with 8 students; Group B average 85 with 6 students. What is the overall average score?

Explanation:
When two groups have different sizes, use a weighted average. Multiply each group’s average by the number of students in that group to get the total points from that group, then divide the combined total points by the total number of students. Group A contributes 8 × 90 = 720 points. Group B contributes 6 × 85 = 510 points. Combined points = 720 + 510 = 1230. Total students = 8 + 6 = 14. Overall average = 1230 / 14 = 87.857..., which rounds to 87.86. So the true overall average is about 87.86. The given 89.00 isn’t consistent with this calculation.

When two groups have different sizes, use a weighted average. Multiply each group’s average by the number of students in that group to get the total points from that group, then divide the combined total points by the total number of students.

Group A contributes 8 × 90 = 720 points.

Group B contributes 6 × 85 = 510 points.

Combined points = 720 + 510 = 1230.

Total students = 8 + 6 = 14.

Overall average = 1230 / 14 = 87.857..., which rounds to 87.86.

So the true overall average is about 87.86. The given 89.00 isn’t consistent with this calculation.

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