Estimating a new standard deviation

Six Sigma – iSixSigma Forums Old Forums General Estimating a new standard deviation

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    I have the following problem. My data set has a mean of 54.6 with an SD of 7.6. This number is higher than the average of 48.0 which was expected on basis of a population. How do I calculate the SD which corresponds to an average of 48.0? My mean shifts from 54.6 to 48.0, but what will happen to my SD of 7.6?
    The data is normally distributed.



    Having trouble with that homework?
    Hint – a feature of a truely normally distributed distribution is that mean and standard deviation are independent. This means standard deviation probably will not change as mean shifts.
    This is one of the real reasons we shold try to understand what distribution we really expect rather than just try to slam everything we get into a normal distribution. Any naturally bounded distribution will not have the convenient feature of mean and standard deviation being independent.

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