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Math Help - expected value, standard deviation

  1. #1
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    expected value, standard deviation

    We have the population of 3000 students. The average height of this population is 180 cm with the standard deviation of 5 cm. We pick 25 random students and measure their height.

    What is the expected value and standard deviation for the average height of this sample?


    I was thinking about this, but my conclusion is that the average will be 180cm with 5 cm standard deviation if we pick a sample of 25 students.

    I know it's wrong but, can someone explain this with mathematical formulas and philosophical idea behind it.

    thank you.
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  2. #2
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    The expected value of the mean is the mean of the population given that the mean is an unbiased estimator.

    The variance of the mean of a sample is greater than zero becuase it is a sample. It should shrink until you have selected the entire population.
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  3. #3
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    I found these formulas, and calculate. Is this correct?

    The mean of entire population is equal to the mean of the sample.
    So the mean of the sample is = 180 cm.

    And standard deviation of a sample is o = o/sqrt(n), o = 5/sqrt(25) = 1

    I am not sure about this. I don' know honest.
    Last edited by Nforce; June 9th 2011 at 01:15 AM.
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  4. #4
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    That's right. Why do you doubt?

    Note: In order to get he variance actually to zero (0) be sampling the entire population, you will need to think about the Finite Population Correction Factor.
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