Introduction

Interpolation is about estimating values from a table of discrete data. For example:

What would the value be at, e.g. ? One of the options would be to draw a straight line between the two points on either side of and then evaluate the equation of this line at .

On the other hand, estimating the value at is more hazardeous, since one now has to use two values on one side of this point to make a prediction. Making an estimate at a value outside the range of the data points is called extrapolation and is far more error prone then interpolation.