# Determining rating scale based off the options

I'm trying to rate each value with a scale. How can I determine the rest of the ratings below?

• less weight is better
• rating scale from 0-10. 10 being the best

• 2.32 lbs - 10
• 2.47 lbs
• 2.55 lbs
• 2.87 lbs
• 2.88 lbs
• 2.9 lbs
• 3.7 lbs
• 3.86 lbs
• 3.9 lbs
• 3.97 lbs
• 4 lbs
• 4.3 lbs
• 5.07 lbs
• 9.12 lbs
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Welcome to Math.SE! If the answer you received meets your requirements, you can mark it as accepted by clicking the check mark to the left of the question. – user53153 Jan 5 '13 at 8:39

You seem want a non-negative decreasing function of mass in pounds where $f(2.32)=10$.

There are a large number of possibilities. One is $$f(x) = \frac{23.2}{x}.$$

For your example values, this gives (to two decimal places)

 x              f(x)
2.32 lbs        10
2.47 lbs        9.39
2.55 lbs        9.10
2.87 lbs        8.08
2.88 lbs        8.06
2.9  lbs        8
3.7  lbs        6.27
3.86 lbs        6.01
3.9  lbs        5.95
3.97 lbs        5.84
4    lbs        5.8
4.3  lbs        5.40
5.07 lbs        4.58
9.12 lbs        2.54

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Thanks Henry. =) – curb Jan 5 '13 at 1:23