Interpolation and Extrapolation

Interpolation and Extrapolation

Interpolation:

• Definition: Interpolation is the estimation of values within a range of known data points.
• Method: It uses known data points to predict values between them.
• Example: If data points for x are given and we use these to create a regression line or curve, estimating the value of y for a specific x within the known range is interpolation.
• Purpose: Used to fill in missing data points or to estimate values within a known data range.

Extrapolation:

• Definition: Extrapolation is the estimation of values outside the range of known data points.
• Method: It extends known data points to predict values beyond the observed range.
• Example: Predicting y for an x value outside the given range of data points is extrapolation.
• Caution: Extrapolation can be risky because it assumes that the trend observed within the known range continues outside that range, which may not always be accurate due to unseen variables or changes in trend.

Key Points:

• Risk: Extrapolation is less reliable than interpolation because it assumes the same trend or relationship continues indefinitely, which may not hold true.
• Applications: Both interpolation and extrapolation are used in various fields such as statistics, economics, engineering, and scientific research to estimate and predict values based on existing data.