Aggregation Math Example 4
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Example 4
hardA school reports average SAT scores improved 20 points. But when broken down by income group, scores dropped for every income group. Explain this as Simpson's Paradox and identify the mechanism.
Solution
- 1 This is Simpson's Paradox: overall scores rise, but each subgroup (income level) scores drop
- 2 Mechanism: the student body composition changed — a larger proportion of students are now from higher-income groups (who score higher on average)
- 3 Even if all groups score slightly lower, replacing low-income students with high-income students shifts the overall mean upward
- 4 Conclusion: the school's improvement is not due to better teaching but to demographic composition change
Answer
Simpson's Paradox: changing demographics (more high-income students) raised the aggregate mean despite per-group declines.
Aggregate statistics can mislead when group composition changes. This is why educational reporting should control for demographics. Overall averages mask whether any individual student group actually improved — the key fairness question.
About Aggregation
Aggregation is the process of combining many individual data values into a single summary statistic such as a sum, mean, count, or proportion.
Learn more about Aggregation →More Aggregation Examples
Example 1 medium
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