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Homework Help: Chebyshev's theorem (statistics)

  1. Sep 20, 2008 #1
    1. The problem statement, all variables and given/known data
    If 100 students take a quiz, use chebyshev's theorem to predict the number of students plus and minus 2 standard deviations from the mean.

    2. Relevant equations
    1-1/k^2 where k is standard deviations

    3. The attempt at a solution
    I think its 75, but I'm not sure...I'm just trying to get this concept down
     
  2. jcsd
  3. Sep 20, 2008 #2

    HallsofIvy

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    Science Advisor

    Don't just memorize formulas, learn what they say! Did you notice that "1- 1/k2" is not even an equation? What is equal to 1- 1/k2?

    1- 1/22= 1- 1/4= 3/4. 3/4 of 100= 75. Now, if "the fraction of trials within k standard deviations of the mean" is what 1- 1/k2 gives, you are completely correct!
     
    Last edited by a moderator: Sep 21, 2008
  4. Sep 20, 2008 #3

    statdad

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    Homework Helper

    Chebyshev's Theorem does indeed state give the percentage data you can expect to find within [tex] \pm k [/tex] standard deviations of the mean, as long as [tex] k > 1 [/tex] (and it is here.
    However, remember that technically the answer is a lower bound, so you the proper response not that the percentage is [tex] 75\% [/tex], but that it is at least [tex] 75\% [/tex].
     
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