What is interpolation used for?

Interpolation is a mathematical technique used to estimate unknown values that fall within the range of a discrete set of known data points. This is particularly useful in various fields, such as engineering and data analysis, where you may have a limited number of measurements or observations, but need to fill in gaps or make predictions for values that lie between those points.

By utilizing interpolation, one can create a continuous function that can approximate the unknown data based on the established points. For instance, if you have temperature readings at specific times, interpolation allows you to estimate the temperature at any other time within that range, leading to more accurate models and analyses.

This approach differs significantly from other options presented. Extrapolation refers to predicting values beyond the range of known data, while arranging data in order focuses on organization rather than estimation. Maximizing performance metrics relates to optimizing outcomes based on available data but does not involve estimating intermediate values between known points. Thus, interpolation is fundamentally about deriving estimates for missing values within the context of existing data.