Extrapolation vs. Interpolation
SAT glossary · Math
Definition
Interpolation estimates a value INSIDE the range of the observed data, where a line of best fit is supported by evidence. Extrapolation estimates OUTSIDE that range, where the model is unverified and the prediction may be meaningless. The SAT tests this by asking for a prediction far beyond the plotted domain - the credited answer recognizes the limit of the model rather than computing confidently.
Extrapolation vs. Interpolation in plain English
When you have scattered data points and draw a line of best fit through them, that line only really has proof behind it for the RANGE of x-values you actually have data for. Interpolation means estimating a value that falls INSIDE that range — somewhere you already have evidence surrounding it on both sides, so the estimate is fairly trustworthy. Extrapolation means reaching OUTSIDE that range, into territory you have zero actual data about — the line might be totally wrong out there, since nothing guarantees the same pattern continues forever. The test loves asking you to predict something way beyond the plotted data, and the correct, careful answer usually points out that such a prediction isn't reliable — rather than just confidently calculating a number as if the model were guaranteed to hold.
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