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January 10th, 2017, 09:05 AM   #1
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Looking for a formula to work out new values based on changing the Max and Min of...

Hi, not sure if this is the best place to ask - please let me know if there's a more suitable forum.

I've got an irregular range of values ranging from -infinity to -1 (randomizes every time). I want to be able to set a new value for the max and min values, and adjust everything in the range so that they stay in position relative to each other.

For example, let's say I have ten values. The lowest is -40 and the highest is -8. I decided I want to make the highest one 0 and the lowest -10. I need to increase the lowest by 30, but the highest by only 8. I then need to increase the numbers in between each by a unique value so that they are in the same position relatively (but over a much smaller range).

Anyone able to offer any assistance?

Thanks.

Last edited by skipjack; January 10th, 2017 at 02:03 PM.
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January 10th, 2017, 01:55 PM   #2
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A simple linear transformation comes to mind. Make two points from the information and find the equation of the line.

In your example, you want $\displaystyle -40$ to map to $\displaystyle -10$ and you want $\displaystyle -8$ to map to $\displaystyle 0$. So make two points $\displaystyle (-40,-10)$ and $\displaystyle (-8,0)$. From these two, make an equation for a line. The slope is $\displaystyle \frac{0--10}{-8--40} = \frac{10}{32} = 0.3125$. So an equation for the line is $\displaystyle y = 0.3125x + 2.5$
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January 10th, 2017, 02:05 PM   #3
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Do the values have to be integers?
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January 11th, 2017, 01:46 AM   #4
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mrtwhs - thanks for the formula! I shall put this into system today and see if it fits what I'm trying to do.

skipjack - no it doesn't. in fact I doubt it would work with just integers.

Thanks guys
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January 20th, 2017, 03:03 AM   #5
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Hi folks,

sorry I haven't had a chance to look into this for a while. mrtwhs - your formula works perfectly for the above criteria, but I was wondering if we could take it a step further. Basically, all the values are variable, so the original highest and lowest, and the new values, can all change. So I need to incorporate this into the formula. I've been trying a few things but can't get my head around it. Any chance you can think of a solution?

Many thanks!
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January 23rd, 2017, 01:06 AM   #6
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I think what you want is this:
Transform a number?
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January 24th, 2017, 06:50 AM   #7
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That's EXACTLY what I'm looking for! thanks weirddave!
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January 24th, 2017, 07:23 AM   #8
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No problem, the most challenging part was trying to find it, I did it longer ago than I thought....
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