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Kid_Learning_C
Kid_Learning_C
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Do we use the standard deviationSD of whole population or SD of just theone sample when applyingto calculate SE of samples means in central limit theorem?

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Kid_Learning_C
Kid_Learning_C
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Do we use the standard deviation of whole population or just the sample when applying central limit theorem?

I'm learning applications on Central Limit Theorem and got really confused with a few points. According to this tutorial, the procedure to apply CLT usually goes like this: enter image description here

So if SD is the population standard deviation, how are we gonna get it?? Isn't the whole population standard deviation what we eventually calculate by applying CLT and analyzing a sample of the whole population? How come the population standard deviation become a prerequisite??

Please tell me this tutorial is wrong.

I think the SD actually refers to the standard deviation of a sample (of some size n), which we can actually get easily. For example:

  1. sample the whole population with a sample size of n (e.g. randomly select 10000 users from the whole population of 10 billions)
  2. calculate the mean of the 10000 measurements.
  3. calculate SE = SD / sqrt(10000), where SD is the standard deviation of the 10000 measurements, instead of the standard deviation of the whole population of 10 billions.

This explanation would make much more sense.

Any thoughts?