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
Let's call the $\displaystyle 20,90$ are the old scores and the $\displaystyle 60,100$ are the new scores.
We can make a linear relationship with the following co-ordinates (old , new) = $\displaystyle (20,60)$ and $\displaystyle (90,100)$ the equation will be in the form
$\displaystyle \text{new score}=m\times \text{old score}+c$ where $\displaystyle m= \frac{100-60}{90-20} = \frac{40}{70} = 0.57$
giving $\displaystyle \text{new score}=0.57\times \text{old score}+c$
now using $\displaystyle (90,100)$ to find the value for $\displaystyle c$
$\displaystyle \displaystyle 100=0.57\times 90+c$
$\displaystyle \displaystyle 100=51.3+c$
$\displaystyle \displaystyle c=48.7$
To scale future scores $\displaystyle \displaystyle\text{new score}=0.57\times \text{old score}+48.7$
The formula I am about to give you is not perfect, but I think it is decent.
Let n=New Grade
Let o=Old Grade
$\displaystyle \displaystyle n=100-0.5(100-O)$
The 20 will end up with a 60, but the 90 will end up with a 95. Sorry if it isn't what you're looking for.
EDIT: too late