Normalize data with a threshold

The graph shows a set of normalized data that i have, from 0 to 1. My process is to put this normalized data set into a colormap in grayscale and show the peaks in white and zeros in black as a nice scale. My problem is that the outliers on the two end of the data set. They turn the colormap complete black and only the ends of the set show some peaks in white. I would like to add a upper limit/threshold on the dataset? if you can understand.

example:

normalized Output that i am looking for it min=2.5 max=7.5

Data = [ 0 1 4 5 8 10 ]
Norm = [ 0 0 0.3 0.5 1 1 ]

All values above 7.5 would be given a 1 and below 2.5 would be be 0. Something like this!

Thank you for your valuable time,

I am new to matlab!

Answer 1

[Walter Roberson]

min_at = 2.5;
max_at = 7.5;
New = max( min( (Data - min_at)./(max_at - min_at), 1), 0)