Normalizing Ranges of Numbers

Date: 04/22/2002 at 08:58:16
From: Stephanie
Subject: Normalizing

Hi, I have several ranges of numbers, for example 5-200 or 200-1500, 
and I want to "normalize" them on a scale of 1-10, 1 being the lowest 
rating and 10 the highest. How do I convert a ranges of 5-200 to a 
scale of 1-10?

Date: 04/24/2002 at 12:48:33
From: Doctor Douglas
Subject: Re: Normalizing

Hi, Stephanie,

Thanks for submitting your question to the Math Forum.

Suppose you have a range or scale from A to B and you want to convert 
it to a scale of 1 to 10, where A maps to 1 and B maps to 10.  
Furthermore, we want to do this with a linear function, so that for 
example the point midway between A and B maps to halfway between 1 and 
10, or 5.5.

Then the following (linear) equation can be applied to any number 
x on the A-B scale:

   y = 1 + (x-A)*(10-1)/(B-A)

Note that if x = A, this gives y = 1+0 = 1 as required, and if x = B,
y = 1+(B-A)*(10-1)/(B-A) = 1+10-1=10, as required.

You can use this equation even if A > B.

You can also adapt this equation to situations where the final scale 
is between any two numbers, not necessarily 1 and 10, but replacing 
them by C and D respectively. The situation x = A will get mapped to 
y = C and x = B will get mapped to y = C+(D-C) = D.

I hope this helps.  Please write back if you need more explanation.

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/