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Thread: Symmetric, Skewed, or Uniform

  1. #1
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    Symmetric, Skewed, or Uniform

    Decide if each distribution of variables is symmetric, skewed, or uniform. Explain

    What I think are the answers are in red---let me know if I am correct. Thank you!


    1) the cost of a high school student's last haircut

    I said symmetric---most students will pay roughly the same amount.



    2) the number of points scored by the winning team in the Super Bowl

    I said skewed---there are a few games where the scores will be signficiantly higher than normal.



    3) how long it took a student run a mile

    I said symmetric----the student will take roughly the same amount of time each time.



    4) the grades on a particulary hard test

    I said skewed----a few outliers doing well, but most people not so well
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  2. #2
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    Re: Symmetric, Skewed, or Uniform

    1) seems correct

    2) seems correct but for wrong reason. Since they are the winning team it is more probable that their score is above the overall average.

    3) seems correct

    4) is correct but I wouldn't label those that do well as outliers. They are just less probable.
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  3. #3
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    Re: Symmetric, Skewed, or Uniform

    For #2, you can literally plot the scores and see the distribution. Depending on what you find, you just need to come up with a reason.

    Super Bowl Winners and Results - Super Bowl History - National Football League - ESPN

    If it is skewed, it is probably skewed in the exact way romsek says, but it seems equally likely to get any score between 20 and 40 (just from a quick perusal of the data), so there may be an argument for calling it a uniform distribution.
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  4. #4
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    Re: Symmetric, Skewed, or Uniform

    Quote Originally Posted by SlipEternal View Post
    For #2, you can literally plot the scores and see the distribution. Depending on what you find, you just need to come up with a reason.

    Super Bowl Winners and Results - Super Bowl History - National Football League - ESPN

    If it is skewed, it is probably skewed in the exact way romsek says, but it seems equally likely to get any score between 20 and 40 (just from a quick perusal of the data), so there may be an argument for calling it a uniform distribution.
    This is probably correct. There's no reason that the scores of the winner's and losers can't both be roughly uniform with the winner's average higher than the loser's.

    My error was in just assuming the distribution had to start at 0.
    Last edited by romsek; Jun 1st 2018 at 09:13 AM.
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    Re: Symmetric, Skewed, or Uniform

    Quote Originally Posted by romsek View Post
    This is probably correct. There's no reason that the scores of the winner's and losers can't both be roughly uniform with the winner's average higher than the loser's.

    My error was in just assuming the distribution had to start at 0.
    I decided to chart it out. I take back my previous assessment. It definitely looks like it is skewed now.

    Symmetric, Skewed, or Uniform-chart.png
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