I'm running an experiment where I'm continuously sampling from a dial hooked into a physiological recorder as a hack because the dial won't interface with the equipment we're using any other way. By way of the connection, the terminal ends of the dial record at 100 and 21.07 with every value (to the hundredths) represented at other positions along its continuum.
Ultimately I need to normalize these values to a range of 0-100 because that's how we're reporting ratings and how we described the ratings procedure to the subjects. I was using this formula - How to normalize data to 0-1 range? - but have a potential problem.
In this situation the (maximum) value 100 represents the rating of 0 and the (minimum) value of 21.07 represents 100. This obviously messes up my final values if I use the data and formula as is.
I tried the following: I first made all values negative (e.g. minimum value is now -100 and maximum is now -21.07) to flip the min-max continuum. I then simply changed the formula in the link to make both subtraction signs into addition signs. This was my final equation.
$$z_i = \frac{x_i + min(x)}{max(x) + min(x)} * 100$$
The problem is, I'm not sure if this is mathematically sound. Looking at the converted values, they don't seem right either from what I know of participant behavior (e.g. the middle values that look like they should be 50 are coming up as 16).
Is there a normalization process I can use specific to my situation where the max value is actually the min?