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  1. #1
    Member princess_anna57's Avatar
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    statistics help

    16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

    This data is the ages of mothers.

    The ages in the sample have presumably been rounded down since eg a mother aged 27 3/4 would have given her age as 27. What effect will this have on your estimate of the mean and standard deviation? Suggest possible corrections to the estimates, distinguishing clearly between the corrected and the uncorrected value.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by princess_anna57 View Post
    16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

    This data is the ages of mothers.

    The ages in the sample have presumably been rounded down since eg a mother aged 27 3/4 would have given her age as 27. What effect will this have on your estimate of the mean and standard deviation? Suggest possible corrections to the estimates, distinguishing clearly between the corrected and the uncorrected value.
    The mean will be biased down by 0.5 years. So a corrected mean would be Sample_Mean+0.5


    RonL
    Last edited by CaptainBlack; August 7th 2007 at 03:07 AM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by princess_anna57 View Post
    16, 21, 21, 22, 22, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 28, 20, 29, 29, 31, 32, 33, 33, 35, 35, 36, 37

    This data is the ages of mothers.

    The ages in the sample have presumably been rounded down since eg a mother aged 27 3/4 would have given her age as 27. What effect will this have on your estimate of the mean and standard deviation? Suggest possible corrections to the estimates, distinguishing clearly between the corrected and the uncorrected value.

    As the Rv is the sum of the two RV's Reported Age and an error epsilon:

    TrueAge=ReportedAge+epsilon

    Now assume Reported Age and epsilon are independent (they are not necessarily but will
    be near enough for our purposes), then:

    var(TrueAge)=var(ReportedAge) + var(epsilon)

    Now epsilon ~U(0,1), so var(epsilon)=1/12. So:

    SD(TrueAge)=sqrt(SD(ReportedAge)^2 + 1/12)

    RonL
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