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/
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