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### Definition of Interpolate

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Date: 10/27/95 at 5:56:19
From: Anonymous
Subject: Interpolate

Could you please define interpolate and give me an example?

I have looked in "The Book of Answers" and it defines interpolate:

Determination of an intermediary value of a function by means of a
sequence of known values of the function.

Mark
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Date: 11/7/95 at 13:0:8
From: Doctor Steve
Subject: Re: Interpolate

Hi Mark,

between two values you already know.  If I gave you a sequence of
numbers and asked you to fill in the missing number you would be
interpolating:

0,1,2, ... ,6

But, since you don't know the rule I'm using, you're only making a
guess.  It often happens, for instance in economics, that you know the
data but you don't know what the formula is that explains why something
happened that way or what the next value will be. I might calculate the
national debt every three months and that might enable me to make a good
guess what it was the two months in between.

Usually when you make an interpolation you are making an assumption
that the behavior you're looking at is predictable or that the amount of
error in your guess can't be enough to prevent you from using it.

In the sequence I gave above you might interpolate a value of 4 and have
some confidence that you wouldn't be more than one off.

So interpolation relies on some assumptions about the behavior of
whatever you're investigating that make it possible for you to guess
values for which you only have information about what happened
"before" and "after".

- Doctor Steve,  The Geometry Forum

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Associated Topics:
Middle School Definitions