Combine Through the Totals, Not the Averages

You'll learnto combine averages through weighted totals, then report the member the question actually asked.

To combine averages you go through the totals, weighted by how many. Watch where the points leak — averaging the averages without weights, building a mixture on the wrong quantity, and reporting a component when the whole mixture was asked.

8 STEPS · 6 QUICK CHECKS · weight by size · track the actual substance · v2

weighted totals

Before you start

What you're looking at

Two bars sized by class — 20 students at avg 80 (1600 points) and 30 at avg 90 (2700) — beside a totals card.

The question

When two classes of different sizes combine, what is their overall average — 85, or something else?

Watch for

The bars grow to different lengths; watch the bigger class pull the combined average toward its own, landing at 86 not 85.

What the symbols mean

Each bar's length is a class size; its point total is size times average; the crossed-out 85 is the unweighted mean.

Step 1 / 8