Joe Celko offers up some thoughts on interpolation:
Interpolation is a mathematical technique which was popular before we had a lot of cheap computing power. The basic idea is that if you’re given a set of data and looking for a value in the same range, you can interpolate it to get a reasonable estimation for the value that is not actually in the set.
If you can find an old calculus, finance, statistics or algebra book, they had lookup tables in the back. Remember that the only computational tools students had back then were pencil and paper or a slide ruler. If you wanted to use a pencil and paper, you had to know what formula to use. If you use the slide ruler, you can only have three decimal places in your answer (yes, there were a couple of over-sized specialized slide rulers which could go as high as four or five decimal places. They were very expensive). But if your slide ruler didn’t have a particular function you were trying to compute, it was hard to get even the three decimal places.
When you try to approximate a value outside the range of your set, that’s called extrapolation. It’s a different topic and requires a slight leap of faith.
Interpolation is a key part of regression techniques. Read the whole thing.