an act or instance of inferring an unknown from something that is known.
Statistics, Mathematics. the act or process of estimating the value of a variable or function outside the tabulated or observed range.

1870–75; extrapolat(e) + -(t)ion

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World English Dictionary
extrapolate (ɪkˈstræpəˌleɪt)
1.  maths Compare interpolate to estimate (a value of a function or measurement) beyond the values already known, by the extension of a curve
2.  to infer (something not known) by using but not strictly deducing from the known facts
[C19: extra- + -polate, as in interpolate]

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Word Origin & History

coined 1872 from extra + (inter)polation; original sense was "insert intermediate terms in a mathematical series." Transferred sense of "drawing a conclusion about the future based on present tendencies" is from 1889.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Cultural Dictionary
extrapolation [(ik-strap-uh-lay-shuhn)]

A mathematical procedure designed to enable one to estimate unknown values of a parameter from known values. A common method of extrapolation is to look at data on a curve, then extend the curve into regions for which there is no data. Extrapolation is often used to predict the future.

The American Heritage® New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Computing Dictionary

extrapolation definition

mathematics, algorithm
A mathematical procedure which estimates values of a function for certain desired inputs given values for known inputs.
If the desired input is outside the range of the known values this is called extrapolation, if it is inside then it is called interpolation.
The method works by fitting a "curve" (i.e. a function) to two or more given points and then applying this function to the required input. Example uses are calculating trigonometric functions from tables and audio waveform sythesis.
The simplest form of interpolation is where a function, f(x), is estimated by drawing a straight line ("linear interpolation") between the nearest given points on either side of the required input value:
f(x) ~ f(x1) + (f(x2) - f(x1))(x-x1)/(x2 - x1)
There are many variations using more than two points or higher degree polynomial functions. The technique can also be extended to functions of more than one input.

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
But his statistical extrapolation suggests that it would not be easy.
Instead, the report's centerpiece is an odd extrapolation of the
  supply-and-demand theory to college education.
The extrapolation process is much more useful in the long term than the plug
  and play process.
Four years and five billion dollars later, the extrapolation seems premature.
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