A test score mean was 52. The top 20% averaged 80, and the bottom 25% averaged 31. What is the mean score of the remaining 55%___________?
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Answer: C. 51.4 approx.
Explanation
Total score sum for all students is calculated using the overall mean of 52. Subtracting the score sums of the top and bottom groups leaves the remaining points. Dividing the remaining score sum by the remaining student percentage yields 51.4. Weighted average equals the sum of all subgroup totals divided by total count. Total score sum equals 100 multiplied by 52 which is 5200 points. Subgroup totals are calculated by multiplying student counts by their respective means.
Educational testing analysis uses weighted group means to evaluate performance tiers. Grading curves often segment student populations into specific percentile brackets. Statistical decomposition of averages helps identify performance gaps in cohorts. Choosing 45 underestimates the average performance of the remaining student group. Choosing 50 is a rounded approximation that misses the precise calculated average. Choosing 54.6 overestimates the average score of the remaining fifty-five percent.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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