Aggregation Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
mediumSimpson's Paradox: Hospital A has a 90% recovery rate overall. Hospital B has 85%. However, for severe cases: A has 70%, B has 75%; for mild cases: A has 98%, B has 95%. Explain the paradox.
Solution
- 1 Hospital B is better for BOTH severe (75%>70%) and mild (95% vs 98%... wait: A=98>95=B) — let's check: for mild cases A=98%, B=95%, so A is better for mild
- 2 Revised: A better for mild (98% vs 95%), B better for severe (75% vs 70%)
- 3 Overall: A=90% > B=85% — A wins overall despite B winning for severe cases
- 4 Paradox: A's higher overall rate is because A sees mostly mild cases (high baseline rate); B sees more severe cases (dragging its average down); comparing without accounting for case mix is misleading
Answer
Simpson's Paradox: aggregated rates can reverse when a confounding variable (case severity mix) is ignored.
Simpson's Paradox occurs when aggregated data reverses the direction seen in subgroups. The overall rate is a weighted average where the weights (case mix) differ between groups. Aggregation can hide critical information about composition.
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 2 easy
Daily temperatures: Mon=20°, Tue=22°, Wed=19°, Thu=25°, Fri=21°. Calculate the weekly mean and expla
Example 3 easyMonthly sales ($thousands): Jan–Mar: 50, 60, 55; Apr–Jun: 80, 90, 85; Jul–Sep: 40, 35, 45. Calculate
Example 4 hardA school reports average SAT scores improved 20 points. But when broken down by income group, scores