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Thread: Scaling grades.

  1. #1
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    Scaling grades.

    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
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  2. #2
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    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 $\displaystyle \displaystyle\text{new score}=0.57\times \text{old score}+48.7$
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  3. #3
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    Thank you very much, very clear and helpful.

    I should remember how to do that. I'm a university graduate. Darn.
    Last edited by mr fantastic; Dec 28th 2010 at 06:06 PM. Reason: m --> r
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  4. #4
    Member rtblue's Avatar
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    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
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