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Thread: Help with this maths questions!

  1. #1

    Default Help with this maths questions!

    This seemingly elementary stats question stumped me. Anyone can help?

    IN a test for eyesight, for which the scores vary from 0 to 6, the table below shows the distribution of these scores for some volunteers who took part in the test.

    Score of < 2: 10 volunteers
    Score of 2: 7 volunteers
    Score of 3: 8 volunteers
    Score of 4: x volunteers
    Score of >= 5: 8 volunteers

    If the mean score is 3, find the value of x.

    The correct answer is 12.

    maths whiz, fire away!

  2. #2

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    Quote Originally Posted by Tweek
    This seemingly elementary stats question stumped me. Anyone can help?

    IN a test for eyesight, for which the scores vary from 0 to 6, the table below shows the distribution of these scores for some volunteers who took part in the test.

    Score of < 2: 10 volunteers
    Score of 2: 7 volunteers
    Score of 3: 8 volunteers
    Score of 4: x volunteers
    Score of >= 5: 8 volunteers

    If the mean score is 3, find the value of x.

    The correct answer is 12.

    maths whiz, fire away!
    For score <2, use the midpoint of 0 and 1: 0.5
    For score >=5, use the midpoint of 5 and 6: 5.5

    Then use the formula Summation f(x) / Sum of x = 3

    To help you further:

    [0.5(10) + 2(7) + 3(8) + 4x + 5.5(8)] / (33+x) = 3

  3. #3

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    Quote Originally Posted by canonsiao
    For score <2, use the midpoint of 0 and 1: 0.5
    For score >=5, use the midpoint of 5 and 6: 5.5

    Then use the formula Summation f(x) / Sum of x = 3
    that's right! I never did much of stats in my whole life of education, is this assumption of using the midpoint a standard practice?

  4. #4

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    Quote Originally Posted by Tweek
    that's right! I never did much of stats in my whole life of education, is this assumption of using the midpoint a standard practice?
    That depends. Since no information of the distribution between 0 & 1 is given, you can generally assume that the 10 people are uniformly distributed between the two. Similarly for between 5 & 6. Sometimes more information about the distribution is known, so in those cases you cannot assume like this.

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