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Math Help - Percentage Weighting formula for student grades

  1. #1
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    Feb 2007
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    Percentage Weighting formula for student grades

    Greetings,

    Let me begin by saying I am not a mathematician, nor even a very good arithmetician. However, I am tasked with explaining to a group of humanities faculty how a piece of software calculates grades based on a method alternately described as "weighted average" or "percentage weighting."

    To keep this as simple as possible, let me pose the following two examples of this grading method.

    A teacher has two components to student assessment, a quiz worth 20% of the final grade and an exam worth 80%. However, he has his own reasons for wishing to ascribe a point value of 400 for the 20% quiz, and 20 for the 80% exam. If a student earns all 400 points of the quiz, he gets a grade of 100, or A+. If he earns all 20 points on the exam, he likewise gets a grade of 100 or A+, and again the same 100 or A+ for the course's final grade.

    The reason I use a large point value for the quiz and a small point value for the exam, is precisely because I do not want an intrinsic relationship between the total points earned as a percentage of total possible points to inform the final grade, but rather the percentage weighting that is assigned to each of the two tests.

    Needless to say, a student who gets 370 out of the 400 point quiz and 16 out of the 20 point exam, will get a lower final grade than 100 or A+. That grade, however, must exactly equal the final grade if I had ascribed 20 points to the 20% quiz and 80 points to the 80% exam for a convenient 100 point total for the course.

    Example Two: Three tests, one quiz of 30 points worth 5%, another quiz of 70 points worth 15%, and an exam of 10 points worth the remaining 80%.

    Can anyone express this percentage weighting in a formula? I am admittedly algebraically challenged, and have filled several sheets of paper trying to figure this out on my own, to no avail.

    Any light you can shed on this computation will be greatly appreciated.

    regards,

    stevenjs
    ____________________________
    "I am but an egg."
    --Stranger in a Strange Land
    Last edited by stevenjs; February 2nd 2007 at 09:13 PM. Reason: Forgot second example
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    Quote Originally Posted by stevenjs View Post
    Greetings,

    Let me begin by saying I am not a mathematician, nor even a very good arithmetician. However, I am tasked with explaining to a group of humanities faculty how a piece of software calculates grades based on a method alternately described as "weighted average" or "percentage weighting."

    To keep this as simple as possible, let me pose the following two examples of this grading method.

    A teacher has two components to student assessment, a quiz worth 20% of the final grade and an exam worth 80%. However, he has his own reasons for wishing to ascribe a point value of 400 for the 20% quiz, and 20 for the 80% exam. If a student earns all 400 points of the quiz, he gets a grade of 100, or A+. If he earns all 20 points on the exam, he likewise gets a grade of 100 or A+, and again the same 100 or A+ for the course's final grade.

    The reason I use a large point value for the quiz and a small point value for the exam, is precisely because I do not want an intrinsic relationship between the total points earned as a percentage of total possible points to inform the final grade, but rather the percentage weighting that is assigned to each of the two tests.

    Needless to say, a student who gets 370 out of the 400 point quiz and 16 out of the 20 point exam, will get a lower final grade than 100 or A+. That grade, however, must exactly equal the final grade if I had ascribed 20 points to the 20% quiz and 80 points to the 80% exam for a convenient 100 point total for the course.

    Example Two: Three tests, one quiz of 30 points worth 5%, another quiz of 70 points worth 15%, and an exam of 10 points worth the remaining 80%.

    Can anyone express this percentage weighting in a formula? I am admittedly algebraically challenged, and have filled several sheets of paper trying to figure this out on my own, to no avail.

    Any light you can shed on this computation will be greatly appreciated.

    regards,

    stevenjs
    ____________________________
    "I am but an egg."
    --Stranger in a Strange Land
    Let us say I understand what you mean.
    [Of course, that means, "Suppose I understand what you mean".]

    Example One:

    Quiz ----- 20% of Final Grade --- 400 points
    Exam ---- 80% of Final Grade --- 20 points.

    a) If student gets 400 points in Quiz, and no matter how much he gets in the Exam, even zero point in the Exam, the student gets 100% Final Grade or A+.

    b) If student gets 20 points in Exam, and no matter how much he gets in the Quiz, even zero point in the Quiz, the student gets 100% Final Grade or A+.

    c) If the student cannot get all 400 points in the Quiz, or all 20 points in the Exam, then you need a formula for the Final Grade of the student.

    Okay.

    Let us say the student manages to get 370 points in the Quiz and 16 points in the Exam.
    (370/400)*20% = 18.5%
    (16/20)*80% = 64%
    Therefore, the Final Grade of the student will be 18.5% +64% = 82.5%

    So, the formula is:
    ((Quiz points)/400)*20% +((Exam points)/20)*80% = Final Grade.

    ------------------------------------------------------------------
    Example Two:

    Quiz #1 ---- 5% of Final Grade ----- 30 points
    Quiz #2 ---- 15% of Final Grade ---- 70 points
    Exam ------ 80% of Final Grade ---- 10 points

    The formula will be:
    ((Q#1 pts)/30)*5% +((Q#2 points)/70)*15% +((Exam points)/10)*80% = Final Grade.


    ---------------------------------------------------------
    Now, if, however I did not understand what you mean, then please forget what I scribbled above.
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  3. #3
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    Joined
    Feb 2007
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    Thank you.

    If I understand you right, it is very simple ;-)

    guess I needed a third sheet of paper.

    Thanks

    regards,

    stevenjs
    __________________
    "I am but an egg."
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