Extrapolation
Extrapolation is a Grade 7 math skill from Yoshiwara Intermediate Algebra used to predict values outside the range of observed data using a mathematical model. While interpolation is more reliable, extrapolation estimates beyond the data range using the same linear or quadratic equation.
Key Concepts
Property Making predictions beyond the range of known data is called extrapolation .
Examples Using the cocoa sales model, $C = 2.5T + 52$, to predict sales at $24^\circ$C is extrapolation. The model gives $C = 8$, an unreasonable result, showing the limits of extrapolation.
An engine's temperature is tracked for 7 minutes. Using a linear model to predict its temperature after 2 hours (120 minutes) is extrapolation and may be inaccurate, as the engine's temperature will not rise indefinitely.
Common Questions
What is extrapolation?
Extrapolation is estimating values outside the range of known data by extending a mathematical model (like a line or curve) beyond the observed points.
How is extrapolation different from interpolation?
Interpolation predicts values within the known data range, while extrapolation predicts outside that range. Extrapolation is less reliable because the model may not hold beyond the data.
When should you be cautious about extrapolation?
Extrapolation becomes unreliable when predicting far outside the data range, since the underlying pattern may change. Always report predictions with appropriate uncertainty.
How do you extrapolate from a linear model?
Use the equation of the linear model and substitute the desired x-value, even if it lies outside the range of the original data.