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Math Help - Need help for homework

  1. #1
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    Question Need help for homework

    Hi all~
    Really need help for below problems:
    1. Please explain when and why we would prefer to use the median instead of the mean as our measure of center.
    2. When there's a largest range in scores but the standard deviation is small, why?

    I appreciate your help^^
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  2. #2
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    Re: Need help for homework

    Hello, Cutiee!

    1. Please explain when and why we would prefer to use the median
    instead of the mean as our measure of central tendency.

    With the mean, one extreme score can drastically affect the average, often distorting the "facts".

    Suppose on one block, there are four families with a mean income of $50,000.
    Would you conclude that any of them need financial aid? .Probably not.'

    Suppose the four families have the following incomes:

    . . \begin{array}{cc}\text{Family} & \text{Income} \\ \hline 1 & 10,000 \\ 2 & 12,000 \\ 3 & 18,000 \\ 4 & 160,000 \\ \hline \text{Total:} & 200,000\end{array}

    We can see that the average is: . \frac{\$200,000}{4} \,=\,\$50,000

    This does not give a true picture of the financial status of this neighborhood.




    2. When there's a largest range in scores but the standard deviation is small, why?

    This can happen if most of the scores are clustered about the mean
    . . and there are only a few extreme scores.


    Here's an extreme example.

    \text{There are 100 scores: }\:0,\,\underbrace{50,\,50,\,50\,\hdots\,50,}_{ \text{ninety-eight 50's}}\,100

    The mean is 50, the range is 100,
    . . but the standard deviation is only \sqrt{50} \:\approx\:7.07

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  3. #3
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    Re: Need help for homework

    Thank you so much Soroban~
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