I have a set of numbers, {2,3,2,4,5,10,9,9,7,12}, and I would like to change the scale.  Want the lowest value to be a 1 and the highest value a 5, and the rest should map accordingly.  Assuming I want to do this linearly, it’s as simple as two mx+b=c and solving for m and b.

Here’s the simple solution:

• s_H is the high bounds of the new scale.
• s_L is the low bounds of the new scale.
• v_max is the max value in your original set.
• v_min is the min value in your original set.

Using these values, calculate m and b:

• m = (s_H – s_L) / (v_max – v_min)
• b = s_H – v_max*m

Now using the m and b values, find the scaled values for each item in your set:

• m*orignal_value + b = scaled_value

Using my example set of {2,3,4,5,7,9,10,12} and scaling between 1 and 5.

• m = (5-1)/(12-2) = 4 / 10 = 0.4
• b = 5 – 12*.4 = 5 – 4.8 = 0.2
• 0.4*x + 0.2 = y

Applying this to the original set, we end up with {1, 1.4, 1.8, 2.2, 3, 3.8, 4.2, 5}.

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