Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Sample Standard Deviation

Announcements Posted on
Become part of the Welcome Squad! Apply here! 28-10-2014
    • Thread Starter
    • 4 followers
    Offline

    ReputationRep:
    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.

    Thanks
    • 3 followers
    Offline

    ReputationRep:
    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.
    • Thread Starter
    • 4 followers
    Offline

    ReputationRep:
    (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?
    • 3 followers
    Offline

    ReputationRep:
    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.
    • Thread Starter
    • 4 followers
    Offline

    ReputationRep:
    (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!

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: May 8, 2012
New on TSR

Halloween 2014

Join the TSR Halloween party...if you dare!

Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.