What is an interpolation and extrapolation?

Question

What is an interpolation and extrapolation?

Answer 1

At the risk of over-simplifying the answer, an interpolation would be estimating a value that lies within the data set.  An extrapolation would be estimating a value that lies outside the data set.

For instance, if the data set contained two points, (1,1) and (3,3), you could interpolate a value of (2,2).  Extrapolating this data set, you could estimate (4,4) or (5,5).

Answer 2

Interpolation and extrapolation can be used in more forms than linear algebra. In a realistic sense, one could interpolate what happened to the price of oil between the dates of 1975 and 1978 given that data can be obtained for reference. Because of this, interpolation is relatively safe. However extrapolation often uses metaphysical means to guess at reality and is risky. Given a relative equation of how oil prices are increasing, one could extrapolate what the price of oil may be in 2024. However, unlike with interpolation, there could be a wide array of variables that no one can know.