Practice Aggregation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Aggregation is the process of combining many individual data values into a single summary statistic such as a sum, mean, count, or proportion.
Going from individual values to totals, averages, or other summaries.
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.
Example 2
easyDaily temperatures: Mon=20°, Tue=22°, Wed=19°, Thu=25°, Fri=21°. Calculate the weekly mean and explain what aggregation loses and preserves.
Example 3
easyMonthly sales (\$thousands): Jan–Mar: 50, 60, 55; Apr–Jun: 80, 90, 85; Jul–Sep: 40, 35, 45. Calculate quarterly totals and annual total. What pattern does aggregation reveal?
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.