Extrapolated

Extrapolated refers to something derived by extrapolation, the act of estimating a value or outcome beyond the known data by extending a trend or pattern. In mathematics and statistics, extrapolation is the process of using a model fitted to observed data to predict values outside the range of the data. It relies on the assumption that the identified relationship continues beyond the observed interval. Interpolation estimates within the range, while extrapolation extends beyond it, which makes it more uncertain.

Common methods include linear extrapolation, where a constant rate of change is assumed; polynomial and spline extrapolation; and model-based approaches such as regression, time-series forecasting, exponential, or logistic models. These methods are chosen based on the data and prior knowledge, and extrapolated results often come with higher uncertainty.

Applications of extrapolation occur across fields. In finance, it is used to project earnings or growth trends. In climatology, it helps forecast future temperatures or emissions scenarios. In engineering, extrapolation can estimate material performance beyond tested limits. In epidemiology, it supports forecasts of case counts. In many domains, extrapolation informs decision making but must be accompanied by appropriate uncertainty estimates.

Limitations and risks include the possibility that trends do not persist, or external factors alter the relationship. Extrapolation far beyond the observed range is particularly unreliable. Reporting should include uncertainty measures such as confidence or prediction intervals and clearly stated caveats.

Etymology: from Latin extrapolare, meaning to push beyond. The term extrapolated describes a value or result obtained by this process.