# Translate percantage increases / decreases into 0 - 100 range?

I am tracking some percentage increase and decrease numbers and I need to plot them on a line graph. However I can only plot them on a line graph with a range of 0 - 100.

What formula would I use translate these percentage values into a range of 0 - 100 if this is possible?

Here is an example dataset:

-15.79, -41.33, -86.59, -41.67, 17.65, 66.67, 191.67, 31.25, 24.39, 0.00

-
What do you want the values between 0-100 to represent? Are they going to be completely arbitrary? Why do you have this restriction of only being able to plot values between 0 and 100 in the first place? –  Chris Taylor May 30 '12 at 10:34
You might want to use the linear transformation $x\mapsto\frac{x+100}{2}$. However, I see no good reason to do this. –  Rasmus May 30 '12 at 10:34
@Chris Taylor The data is going to be used in a program. The service used to generate the graph has this restriction of values between 0 - 100. The values should represent the percentage movements. I just don't know how to transform the numbers and scale them exactly. For example if I had a range of -50 to 50 I could transform the values to o - 100 and a value of 0 would be plotted at 50. How do I accurately do this without know the upper and lower limits being fixed? –  lanks May 30 '12 at 10:45

The maximum is 191.67 and the minimum -86.59 (though presumably the minimum could in theory go down as far as -100). So one possible linear transformation might be to have the top of the graph representing +200 and the bottom -100 using $$f(x) = \frac{x+100}{3}$$ which would give points to plot at
28.07, 19.5567, 4.47, 19.4433, 39.2167, 55.5567, 97.2233, 43.75, 41.4633, 33.3333

More generally, if $M$ is the maximum or some convenient number above it and $m$ the minimum or some convenient number below it then you can use $$f(x)=100 \times \frac{x-m}{M-m}$$ or if you want it the other way up $$f(x)=100 \times \frac{M-x}{M-m}.$$