Normalizing a list of values between a range

Question

So let's say I have something like this:

values = [10.0, 12.0, 14.0, 16.0, 18.0, 20.0]

I basically want to multiply everything in the list by a power of 2, but then normalize it back down to range it was in.

This is how I was attempting to do it, but not getting the results I expected.

minVal = min(values)
maxVal = max(values)

normValues = [((q**2)-minVal)/(maxVal - minVal) for q in values]

Any help would greatly be appreciated!

Answer 1

It is clearly possible that when you square each value in your list and normalize them back, you cannot get them back in the same range. For example : if you take [2, 3, 5]. After squaring, you will get [4, 9, 25]. You can normalize this in a way such that the range is between 0 to 1 i.e you divide all the elements by the largest value getting [0.16, 0.36, 1]. I don't think this list can be scaled back such that the range becomes the same as before. Correct me if I'm wrong.