# Statistics and clarification of Central Limit Theorm

If I have 1,000 participants ranking on a scale of 1 to 10 regarding some object how do I interpret the confidence level and margin of error of the resulting rank? I am used to of seeing 99% confidence level and 4% margin of error type notations so how do these numbers play into my sample case? And how does the resulting rank fit with the large n and Central Limit Theorem?

I am weighting each rank against the percentage of total participants to get a final result.

And could you also explain what a response distribution is related to this scenario and why it is best to assume 50%?

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from wikipedia: >central limit theorem (CLT) states that, given certain conditions, the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed.[1] –  yiyi Oct 29 '12 at 22:59

## 1 Answer

Your question is a little vague, but essentially standard error, standard divination, etc. become negligible when the sample size is sufficiently large. The standard error is equal to the standard deviation divided by the square root of the sample size, which is a result from CLT.

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What does the margin of error apply to? and How (some explanation here maybe) is the central limit theorem fulfilled in this case? –  nvdkgm Oct 29 '12 at 23:15
You should rephrase your question before you downvote my answer. Like I said, your standard error is small because your sample size is large. –  glebovg Oct 29 '12 at 23:17
@glebovg I also am a bit unclear of why a certain standard of error is required, there is a relationship that if the number of samples increases then the error goes down. Is this what the asker is after? –  yiyi Oct 29 '12 at 23:23
@MaoYiyi To be honest, I am not sure what the question is. –  glebovg Oct 29 '12 at 23:24
If $n$ is large, margin of error should be small that is all I can tell you. I am still confused. –  glebovg Oct 29 '12 at 23:57