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Math Help - Averages

  1. #1
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    Averages

    A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?

    Alright, apparently I was wrong...

    I thought you'd take both of the averages of the two groups and then divide by two but apparently that's wrong.

    70+80=150/2=75. The correct answer, it says, is 77.
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  2. #2
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    Quote Originally Posted by A Beautiful Mind View Post
    A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?

    Alright, apparently I was wrong...

    I thought you'd take both of the averages of the two groups and then divide by two but apparently that's wrong.

    70+80=150/2=75. The correct answer, it says, is 77.
    I can see why you would think to do it that way, but the correct way to calculate the average is total score/ total number of students.

    So for the juniors, let  x be their total score. Then we know that \frac{x}{35} = 80 ~ \Rightarrow ~ x = 2800

    For the seniors, let y be their total score. Then similarly \frac{y}{15} = 70 ~ \Rightarrow ~ y = 1050

    So the correct average for the 50 students as a whole is \frac{x+y}{50} = \frac{3850}{50} = 77<br />
    hope this helps,
    pomp.
    Last edited by pomp; July 18th 2009 at 04:24 PM. Reason: typo
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  3. #3
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    Yeah, I just did it this way.

    35/50 = 70% = 0.7
    15/50 = 30% = 0.3

    = 0.7(80)+0.3(70)

    = 56+21

    = 77
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  4. #4
    MHF Contributor matheagle's Avatar
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    This is what you called a weighted average.
    If the two sample sizes were equal, then you could just average the two averages.
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  5. #5
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    Quote Originally Posted by A Beautiful Mind View Post
    A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?

    Alright, apparently I was wrong...

    I thought you'd take both of the averages of the two groups and then divide by two but apparently that's wrong.

    70+80=150/2=75. The correct answer, it says, is 77.
    If there was 4 students in one class (average mark 95%) and 400 students in the other class (average mark 25% - a large class of dopes) would you still be inclined to do it this way and say that the average score for all students was 60% ....
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    No, of course not. I've just been accustomed to taking the arithmetic mean usually and I guess I was a little confused when it came to how it was 77.
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  7. #7
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    ??? That is the arimetic mean!
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    ...what I was referring to was the idea of this:

    I saw the averages of both at first and thought, hey, since they took the average of both of them maybe I can just put them together like you do with a group of test scores and then divide them by how many you have...

    So I had 2 averages, added them together, and then divided by how many I had and that wasn't the case I figured out later on. I did before get the numbers in the thousands like in the first post but I wasn't sure you did it that way and just took the way I originally had and known to use all this time...

    I got 75, which was surely an answer choice but not the right one.
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  9. #9
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    What you did was the arithmetic average of those two numbers. What the question was asking for was the arithmetic average of all 50 test scores.
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  10. #10
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    I know, I figured that out, lol.
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