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Sample Standard Deviation

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    Say you're given a question where you're given a question like: A vending machine machine is supposed to dispense chocolate goodness with an average weight of xx and a s.d. of xx.

    Then they give you some sample data and you're supposed to conclude whether the standard deviation is accuarate.

    Why do you use the sample standard deviation and why can you not take the standard deviation of the sample? I'm not sure why you can't.

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    I dont understand your question. Are you asking why you divide by (n-1) rather than dividing by n?

    If so, the difference between the two estimators is very minor in sufficiently large data sets. However dividing by n gives you a biased estimate of the standard deviation, so using (n-1) is usually preferred since its unbiased. I dont know what level of statistics youve studied up to, but any elementary textbook should show you how to compute the expected value of the estimator which divides by n (which is the maximum likelihood estimate) and if you do the calculation you will find it has a bias and that dividing by (n-1) instead removes it.
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    (Original post by poohat)
    I dont understand your question. Are you asking why you divide by (n-1) rather than dividing by n?

    If so, the difference between the two estimators is very minor in sufficiently large data sets. However dividing by n gives you a biased estimate of the standard deviation, so using (n-1) is usually preferred since its unbiased. I dont know what level of statistics youve studied up to, but any elementary textbook should show you how to compute the expected value of the estimator which divides by n (which is the maximum likelihood estimate) and if you do the calculation you will find it has a bias and that dividing by (n-1) instead removes it.
    Aye, exactly what I meant. So basically, if you're given a small sample, it would be better to use the sample standard deviation as it removes the bias, right?
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    Generally, most statisticians will prefer an unbiased estimator, most of the time. Using the sample standard deviation is the normal way of doing things, yes.
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    (Original post by poohat)
    Generally, most statisticians will prefer an unbiased estimator, most of the time. Using the sample standard deviation is the normal way of doing things, yes.
    I'm no statistician - hate the module!

    Thanks for the help!

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