Editing Extrapolation (section)

{{short description|Method for estimating new data outside known data points}}
{{for multi|the journal of speculative fiction|Extrapolation (journal)|the John McLaughlin album|Extrapolation (album)|the Apple TV+ series|Extrapolations (TV series)}}

In [[mathematics]], '''extrapolation''' is a type of [[estimation]], beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to [[interpolation]], which produces estimates between known observations, but extrapolation is subject to greater [[uncertainty]] and a higher risk of producing meaningless results. Extrapolation may also mean extension of a [[wikt:method|method]], assuming similar methods will be applicable. Extrapolation may also apply to human [[experience]] to project, extend, or expand known experience into an area not known or previously experienced. By doing so, one makes an assumption of the unknown<ref name="merrian-webster">[http://www.merriam-webster.com/dictionary/extrapolation Extrapolation], entry at [[Webster's Dictionary|Merriam–Webster]]</ref> (for example, a driver may extrapolate road conditions beyond what is currently visible and these extrapolations may be correct or incorrect). The extrapolation method can be applied in the [[interior reconstruction]] problem.

[[Image:Extrapolation example.svg|thumb|right|Example illustration of the extrapolation problem, consisting of assigning a meaningful value at the blue box, at <math>x=7</math>, given the red data points]]