Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sample and population variances: elementary question

  1. Jan 31, 2013 #1


    User Avatar
    Gold Member

    Given a sample of a normally distributed population, then the sample variance ≈the population variance divided by the sample size. Nice. However, if one now increases the sample size to the population, this becomes that the population variance ≈ the population variance divided by the population size, which is absurd. What elementary concept am I missing here? Thanks in advance
  2. jcsd
  3. Jan 31, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

  4. Jan 31, 2013 #3
    In statistics the idea is that you have a population and are trying to figure out its parameters. So you take a sample to get an estimate.

    The population parameters are assumed to be constants. The sample parameters are random variables, because they will vary from sample to sample.

    You are also confusing the sample variance with the variance of the sample mean.

    The variance of the sample mean (usually) converges to zero, while of course the population variance does not. The sample variance converges to the population variance.

    This stuff is confusing, but it is important to get it straight or you will never understand statistics. So good for you for asking.
    Last edited: Jan 31, 2013
  5. Jan 31, 2013 #4


    User Avatar
    Gold Member

    From ImaLooser
    You hit the nail on the head! Perfect. I now understand. Thanks very much, ImaLooser.
    And thanks also to Simon Bridge for replying.
  6. Feb 15, 2013 #5


    User Avatar

    Sample variance is NOT equal to population variance divided by sample size.
  7. Feb 15, 2013 #6


    User Avatar
    Gold Member

    Yes, I know, that was the absurdity in my mini-proof that something was wrong with the original assumptions. That is, if I make a point that X is wrong because it leads to 1=0, then saying that 1≠0 is missing the point.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook