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Math Help - Business Statistics: Tchebysheff's Theorem

  1. #1
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    Unhappy Business Statistics: Tchebysheff's Theorem

    This is a three part question and I'm stuck on the third part, if someone could please help.

    Consider the following set of sample data:
    78 121 143 88 110 107 62 122 130 95 78 139 89 125

    a. Compute the mean and the standard deviation for these sample data.

    answer is mean=106.2142857 standard deviation=24.09854344

    b. Calculate the coefficient of variation for these sample data and interpret its meaning.

    answer is coefficient of variation=22.68860848
    I don't know what it means by interpret it's meaning....

    c. Using Tchebysheff's Theorem, determine the range of values that should include at least 89% of the data. Count the number of data values that fall into this range and comment on whether your interval range was conservative or not.
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    Quote Originally Posted by lisa1984wilson View Post
    This is a three part question and I'm stuck on the third part, if someone could please help.

    Consider the following set of sample data:
    78 121 143 88 110 107 62 122 130 95 78 139 89 125

    a. Compute the mean and the standard deviation for these sample data.

    answer is mean=106.2142857 standard deviation=24.09854344

    b. Calculate the coefficient of variation for these sample data and interpret its meaning.

    answer is coefficient of variation=22.68860848
    I don't know what it means by interpret it's meaning....

    c. Using Tchebysheff's Theorem, determine the range of values that should include at least 89% of the data. Count the number of data values that fall into this range and comment on whether your interval range was conservative or not.
    You require the value of \alpha such that \Pr(|X - \mu| \leq \alpha) \geq 0.89 \Rightarrow \Pr(|X - \mu| \geq \alpha)\leq 0.11 .

    Tchebysheff's Theorem (one of the equivalent forms): \Pr(|X - \mu| \geq \alpha) \leq \frac{\sigma^2}{\alpha^2}.

    So you require the value of \alpha such that \frac{\sigma^2}{\alpha^2} = 0.11.
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