Results 1 to 5 of 5

Math Help - Several basic statistics questions

  1. #1
    Junior Member
    Joined
    Sep 2013
    From
    Ohio
    Posts
    45

    Several basic statistics questions

    Hi can you please help me with some basic questions? I'm self-teaching and I want to make sure I'm not messing up!
    1. When you have the sampling distribution of the mean of any distribution, by applying the central limit theory you can calculate the standard error by sigma (or estimated sigma, if you don't know sigma) by the root of the # of your observations. When you keep your sample size the same and increase the number of trials, you approach a normal distribution with a smaller and smaller SD of the mean. If your sample size is 1 you don't get a nice bell shape for the mean sample size though if your population is not bell-shaped. Like when you have a sample of 1 you're just going to get closer and closer to the actual distribution. Is what I wrote right?
    2. If your population is not bell-shaped (let's say very positively skewed), what minimum sample size do you need to get a bell-shaped distribution of the sample mean? Can it be as small as 2 as long as you have A LOT of simulations (a million, 5 million, 10 million, maybe more)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    600
    Thanks
    165

    Re: Several basic statistics questions

    You don't pick a sample size and repeatedly find the mean with many sets of data with that sample size. You put all of your samples into one data set and the size of that is the sample size that affects the accuracy of the sample mean. Does this clear things up?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2013
    From
    Ohio
    Posts
    45

    Re: Several basic statistics questions

    Thanks for responding. I wanted to know if my first statement was correct from a theoretical standpoint.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2013
    From
    Ohio
    Posts
    45

    Re: Several basic statistics questions

    I know in reality you don't do that, but I was just curious.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Oct 2012
    From
    Ireland
    Posts
    600
    Thanks
    165

    Re: Several basic statistics questions

    Yes it is correct from a theoretical standpoint. If you collected 50 samples and found the sample mean, then 50 more samples and found the new sample mean, and repeated that again and again; if you plotted all your sample means on a histogram then it would look like a bell curve.

    As for your second question, if you are not sampling from a bell-shaped population then usually it is recommended to have 30 or 50 samples before using the normal distribution approximation. For some distributions there are better rules of thumb to use for the sample size.
    If you were sampling from a binomial distribution where the value can only be 1 or 0 then if you just took 2 samples the sample mean would be either 0 or 0.5 or 1. So if you repeatedly took 2 samples 1 million times then the histogram would just be three points and not like a bell curve at all.
    Last edited by Shakarri; May 13th 2014 at 05:52 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. basic statistics question help please
    Posted in the Statistics Forum
    Replies: 0
    Last Post: August 22nd 2012, 03:05 PM
  2. Basic Statistics
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: June 30th 2008, 06:51 AM
  3. Basic Statistics
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: April 23rd 2008, 09:45 PM
  4. statistics; very basic
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 8th 2007, 10:27 AM
  5. Basic Statistics. Help please
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: September 26th 2006, 03:30 PM

Search Tags


/mathhelpforum @mathhelpforum