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General math to find average

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  1. Dec 4, 2014 #1
    • Missing template due to originally being posted in different forum
    the question statement is


    2. In a course, a student's final exam is weighted twice as heavily as his midterm exam. If a student receives a score of 84 on his final exam , 90 on his midterm, what is the average for his courses?

    now i am pretty confused should I have to know the total marks for the exam. I can keep final score 84 and half the midterm to 45 and then average them. is this the right way to do it?

    and i got an answer of 64.5
     
    Last edited: Dec 4, 2014
  2. jcsd
  3. Dec 4, 2014 #2

    Mentallic

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    If the final is weighted twice as heavily as the midterm, then you can think of it as being 3 exams in total with all equal weighting, where 2 of them are 84, then find the average of those.

    So you have

    [tex]\frac{2*84+90}{3}=\frac{2}{3}84+\frac{1}{3}90=86[/tex]

    Your approach was almost there, but you missed the detail that since you had 1 score of 84 and then half a score of 90 (in a sense) then to average these you would've had to have divided by 1 and a half.
     
  4. Dec 4, 2014 #3

    SteamKing

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    The 'average' should wind up somewhere between the highest and lowest scores, whether there are two scores or twenty scores.
    Under your scheme, a student whose individual scores were solid Bs (84 and 90) wound up failing the course. (64.5) :L
     
  5. Dec 16, 2014 #4
    You could also solve it in your head using : since the weights are in the ratio 1:2 therefore 2 times decrease in 90 corresponds to 1 time increase in 84
    Therefore,
    84-----90
    85------88
    86------86(which is the desired answer)
     
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