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Math Help - Empirical rule help

  1. #1
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    Empirical rule help

    Not sure how to approach this question.
    I've calculated the following already, sample standard deviation of the data is 1.449931 and the sample mean is 2.366667.
    any help is appreciated.

    The empirical rule states that if a distribution is approximately bell shaped, then approximately 95% of the
    samples will fall between two standard deviations of the mean.


    Calculate the proportion of the sample that is within two standard deviations of the mean and comment on
    its closeness to the 95% estimate from the empirical rule.
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  2. #2
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    Re: Empirical rule help

    Quote Originally Posted by dangitnghia View Post
    Not sure how to approach this question.
    I've calculated the following already, sample standard deviation of the data is 1.449931 and the sample mean is 2.366667.
    any help is appreciated.

    The empirical rule states that if a distribution is approximately bell shaped, then approximately 95% of the
    samples will fall between two standard deviations of the mean.


    Calculate the proportion of the sample that is within two standard deviations of the mean and comment on
    its closeness to the 95% estimate from the empirical rule.
    You have to find the % of your samples that fall within 2 standard deviations of your sample mean. That should be about 95%.

    So use excel or whatever to count up the number of samples that are in the range [2.37 - 1.45, 2.37+1.45] and divide it by the total number of samples.

    That should be about 0.95.
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  3. #3
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    Re: Empirical rule help

    Quote Originally Posted by romsek View Post
    You have to find the % of your samples that fall within 2 standard deviations of your sample mean. That should be about 95%.

    So use excel or whatever to count up the number of samples that are in the range [2.37 - 1.45, 2.37+1.45] and divide it by the total number of samples.

    That should be about 0.95.
    For 95% of samples to fall in between two standard deviations. shouldn't I use (x -+ 2s)? where x is the sample mean and s is the sample standard deviation.

    the range would then be [2.37 - (2) 1.45, 2.37+ (2)1.45]
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  4. #4
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    Re: Empirical rule help

    here is the data.
    0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 5 5

    100% of the data would fall in the range calculated above.
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  5. #5
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    Re: Empirical rule help

    Quote Originally Posted by dangitnghia View Post
    here is the data.
    0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 5 5

    100% of the data would fall in the range calculated above.
    sorry. You're right and it does.
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