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Thread: calculating means and standard deviation from confidence interval

  1. #1
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    Question calculating means and standard deviation from confidence interval




    Is there anyway to calculate mean and standard deviation if we are given the 95% confidence interval?
    I have the following interval 1.339-13.833
    I know that the sample size is 128.
    I know that the way to calculate a two-tailed confidence interval is

    sample mean +/- Z(alpha/2) * s/sqrt(n)

    If I put in
    1.330=xbar - z (.05/2) * s/sqrt (128)
    13.833 = xbar + z (.05/2) * s/sqrt (128)

    How do I solve for mean and sd at the same time?
    Is this problem even solvable?

    Thanks!

  2. #2
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    hello
    your answer is true but you should put z (.05/2) in two equation
    z (.05/2) =1.96
    now you can solve two equation and will get mean and sd

  3. #3
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    As elnaz said, you can solve this set of equations for s and xbar.

    Solve one of the equations for xbar:

    xbar = 13.833 - 1.96*s/sqrt(128)

    substitute this xbar into the second equation:

    1.330 = (13.833 - 1.96*s/sqrt(128)) - 1.96*s/sqrt(128)

    solve this equation for s:

    s = (13.833-1.330)*sqrt(128)/(2*1.96) = 36.0855

    plug s into either equation and solve for xbar to get:

    xbar = 13.833 - 1.96*(36.0855)/sqrt(128) = 7.583

    ~Matt

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