Weighted mean
SAT glossary · Course Foundations
Definition
Not the mean of the means: three tests averaging 80 and two averaging 90 give (3(80)+2(90))/(5) = 84, not 85, because the 80 carries more weight. Convert to totals; averaging the averages is the planted error.
Weighted mean in plain English
A weighted mean is NOT the same thing as just averaging a bunch of separate averages together — you have to account for how many items went into each individual average. For example: if three tests average 80 points and two OTHER tests average 90 points, the OVERALL average across all five tests is (3(80)+2(90))/(5)=84 — not simply 85 (which is what you'd wrongly get by just averaging 80 and 90 together, ignoring that the group of 80s has more tests in it and therefore counts for more). The safe method is to always convert back to TOTALS (multiply each average by its count) before combining anything — averaging the averages directly, without weighting, is exactly the planted mistake these questions are testing for.
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