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Math Help - 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
    Master Of Puppets
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    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
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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; December 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 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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