I am studying CLT and I had a doubt.

I understand that sampling distribution has a mean same as population mean and std.dev as 6/sqrt(n) where n is sample size. Each point on X axis of Sampling dist is a mean of a random sample of sample size N. And by Z scores we can find the probability of a random sample having a particular mean.

I did few exercises on finding the probability. However, one particular question made me feel I still don't know CLT.

If you have taken a random sample with 121 observations from a population with 625 observations, mean=34 and standard deviation=4.1, what would be the standard deviation of that sample?

The answer to this exercise is 4.1/sqrt(121).

My doubt is that this formula applies to a sampling distribution. We are randomly taking samples which can take any value of mean and std.dev. How can we say that a std deviation of a random sample is same as that of sampling distribution. While I believe that more no of sample sets will have a mean same as that of Population but how can we say anything about std deviation. We can only confirm the standard deviation of a sampling distribution. I feel as if that answer to the above question means that we can assume sampling distribution as a distribution of one Random Sample (which I believe isn't correct).

Someone please correct my notions.

Thanks Ramneek Singh

  • $\begingroup$ Could you please explain the last part of the bold faced passage, namely, what do you mean by "what would be the standard deviation of that sample"? Also, CLT is used make statements about the asymptotic behavior of certain quantities ... I hope these help a bit :-) $\endgroup$ – Math-fun Feb 22 at 11:26
  • $\begingroup$ Yup. That is my understanding too and I believe that the question (in bold) in itself isn't correct $\endgroup$ – Ramneek Singh Kakkar Feb 23 at 10:26

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