Mixtures and weighted averages

When two groups of different sizes are combined, the combined average sits closer to the larger group's average. You cannot average the averages; you have to work with totals, or weight each average by its group size.

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LearnWhat it is, how to spot it, a worked example, and where it goes wrong.
Practice — 3-point ladderNo problems written at this tier yet.Nothing written at this tier yet
Practice — 4-point ladder2 problems. Three in a row finishes it.0/3 in a row · 0/2 solved
Practice — 5-point ladder1 problem. Three in a row finishes it.0/3 in a row · 0/1 solved
Skill quizFinish every ladder that has problems first.Finish the ladders above first

Before and after

Needs first

NUM-11Ratio as parts of a whole NUM-15Means, and working backwards from a mean

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In official papers

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