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I'm sorry if this questions sound stupid or something but I'm really interested in this.

I know how to graph some numbers and then find out values of some point in it, however I'm wondering if there is some mathematical formula that can help me to find that without drawing it.

Let's say I have some values like in the picture, I need to know value of x on 40%, is there any mathematical way of doing it? Any formula for it so I can, maybe write computer program that does this for me?

enter image description here

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I assume you have drawn it and noticed that the value at $100\%$ doesn't really look nice. Are you sure about that? –  draks ... Jan 19 '12 at 22:10

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up vote 6 down vote accepted

There are infinitely many formulas that fit the five data points you have given, and they give every value at 40 from minus infinity to infinity.

Things are different if you have some reason to think that your data fits some particular kind of formula, like a polynomial of low degree, or an exponential or logarithmic curve - but only you know where the data came from, so only you can tell if there's reason to expect some particular sort of formula.

Absent a formula-type, there are many ways available to make a guess at missing values. The general problem is called "interpolation", and one popular method is called "linear least squares". You should be able to find lots of information on those, and then report back to us on what you have found.

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Thanks, will do. –  Qmal Jan 19 '12 at 21:52

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