How do I create an index where a low number equals a high score, as below?

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Can you help? If $0.6 = 10$ and $30 = 1$, what does $3.3$ equal and what does $1.62$ equal? Is there a formula to this and if so what is it, please? This would enable me to calculate any number between $0.60$ and $30.00$ (to two decimal places) and correlate it to a number between $10$ and $1$ (to one decimal place).

Thank you,

Steve

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Sure. This is easily done if you want a linear relationship. If you want a linear relationship, you could use the (approximate) formula $$\text{index}=-.306*\text{value}+10.18$$

Thus, you could plug in 3.3 and see that it would give you about 9.17 $$9.17\approx(-.306)(3.3)+10.18$$

However, it should be noted, a linear relationship is just one example of how you could do this. Like, those final few tenths as you near 0.6 could be more valuable than those near 30 (on the input).

EDITING TO ADD:So, reading your comments, there's really no "correct" answer. Just depends on your tastes. But here's one you could play around with and see if it gives reasonable answers. $$y=\frac{5x+22}{5x-\frac{1}{2}}$$

Where $x$ is your input $(0.6\text{ or }30)$ and $y$ is your index $(10\text{ or }1)$ enter image description here