Aggregation Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Aggregation.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept 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.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Aggregation simplifies but loses detail—Simpson's paradox shows the danger.

Common stuck point: Patterns can reverse when you aggregate—always check subgroups.

Worked Examples

Example 1

medium
Simpson'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. 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. 2
    Revised: A better for mild (98% vs 95%), B better for severe (75% vs 70%)
  3. 3
    Overall: A=90% > B=85% — A wins overall despite B winning for severe cases
  4. 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.

Example 2

easy
Daily temperatures: Mon=20°, Tue=22°, Wed=19°, Thu=25°, Fri=21°. Calculate the weekly mean and explain what aggregation loses and preserves.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Monthly 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 2

hard
A 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.
← Back to Aggregation Practice Mode

Related Concepts

MeanData (Abstract)

Background Knowledge

These ideas may be useful before you work through the harder examples.

meandata abstract