Center and Spread
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalThe mean, median, mode, and range compress the same data in different ways, and the SAT tests whether you know which does what. The points leak in the mechanics, an outlier expected to move the median or spare the mean, in the recipe, a median taken without sorting or an even count's middle pair left unaveraged, and at the end, in the name: a flawless mean reported for a median question.
These patterns aren't really about whether you can average numbers. They're about whether you know the mean follows totals while the median follows position, whether the sort happened before the middle was taken, and whether the measure you reported is the one the question named.
The work
4 ways in · any order
Lesson
Center and Spread
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Track how outliers drag the mean and spare the median, run the sort-then-middle recipe exactly, work add-and-remove questions through the total, and report the named measure. The lesson works the method and the three patterns that derail it, and it saves the trap for last: the right computation for the wrong statistic.
Diagnostic
10-item topic check
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Ten items across the three patterns: outlier effects on mean versus median, medians without sorting or with fumbled even counts, and the wrong measure reported. A mix of raw data sets, add-and-remove means, and choose-the-measure judgments. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.