I need to scale some tests. The highest grade is a 90 and the lowest is a 20. I want to scale them so that the lowest is a 60 and the highest is a 100. How do I make an equation that will do this?

Thanks

2. Let's call the $20,90$ are the old scores and the $60,100$ are the new scores.

We can make a linear relationship with the following co-ordinates (old , new) = $(20,60)$ and $(90,100)$ the equation will be in the form

$\text{new score}=m\times \text{old score}+c$ where $m= \frac{100-60}{90-20} = \frac{40}{70} = 0.57$

giving $\text{new score}=0.57\times \text{old score}+c$

now using $(90,100)$ to find the value for $c$

$\displaystyle 100=0.57\times 90+c$

$\displaystyle 100=51.3+c$

$\displaystyle c=48.7$

To scale future scores $\displaystyle\text{new score}=0.57\times \text{old score}+48.7$

3. Thank you very much, very clear and helpful.

I should remember how to do that. I'm a university graduate. Darn.

4. The formula I am about to give you is not perfect, but I think it is decent.

$\displaystyle n=100-0.5(100-O)$