Data Definition:
A set of scores with size N of range(0 to 10) of decimal values:
[0.5, 0.8, 3.5, 8.5, 9.5, 9.9]
or
[7.7, 7.7, 7.7, 7.7, 7.7, 7.7, 7.7, 7.7, 7.7, 7.8]
Problem Definition:
A company has access to a simulation that audits products and spits out a score for each product ranging from 0 to 10. E.g the score of 5 for product 'X' will provide the following rating to a customer.
The company wants to ammend the score to do two things:
Inflate results toward a ceiling value. Each score should fit closer to 10 even though its real score is not necessarily 10.
o′ = f(o +w) (where o' is new score, o is original and w is a weight)
Maintain distance semblance to the original set.
Given o′A , oA, o′B , oB where o'X is new score and oX is old score the relative distance should remain the same between A and B.
Relative distance meaning if the original distance for A -> B was 1 but after step 1 it became 0.1. Distance between C -> D should be scaled the same. So if original distance between C and D was 1 the new distance would also be 0.1
The end goal is to fit the ratings so they are closer to 10 while still maintaining the scaled value differences for each value in the set
What would be a good approach or function to accomplish this?
I can provide more details or answer any questions if needed