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Interpolation is predicting values within a range of data.

Extrapolation is predicting values outside a range of data.

Is there a word that encompasses both meanings, such that I could use it to refer to one, the other, or both? I am looking for a word in the context of statistics and data science. I have considered "predict", "estimate", "infer", and "model", but I think these are a bit general and overloaded. I'm hoping to find a word that specifically encompasses extrapolation and interpolation without including much more than that. My thesaurus has provided rather nontechnical synonyms for both, and I would love to find a word that sounds roughly as technical as extrapolation/interpolation.

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    infer? But then you must have considered this already, have you?
    – user405662
    Commented May 13 at 17:23
  • @user405662 I'm hoping for something a little more technical, more in lines with extrapolation/interpolation.
    – Tashus
    Commented May 13 at 17:24
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    I suggest that in "normal" English, extrapolation is can be used to calculate any value using data from known / measured values. It's only in certain specialized contexts (such as predicting the Earth's future climate, or the future price of Bitcoin) that it might be useful to distinguish interpolation as a special (more reliable?) case of extrapolation. But if you want to get really precise, arguably you might need separate terms for extrapolated values from before you have measurements (potentially verifiable) and future extrapolated values (not so easily checked! :)
    – FumbleFingers
    Commented May 13 at 17:39
  • There's also intrapolation. Think about international (between nations) and intranational (within a nation). Where extranational also exists. (I thought about that a bit, but in the end, gave up with brain-ache! :)
    – FumbleFingers
    Commented May 13 at 17:52

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I suggest that interpolation and extrapolation are both a form of projection.

project
verb
to calculate an amount or result expected in the future from information already known

From Cambridge Dictionary.

In statistical science, data is projected for results that weren't actually measured.

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    Thank you. This seems to be a great choice. I'll accept in 24 hours.
    – Tashus
    Commented May 13 at 17:44
  • I wouldn't use project/projection for interpolated data if the point(s) of interpolation are in the past.
    – DjinTonic
    Commented May 14 at 1:07

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