# Central limit theorem with unknown variance

In my experiment I compute the average Latency of operations per second.

Now, I would like to define N, i.e: how many times do I need to run my experiment to compute a close to real average latency.

I figured that I could apply the CLT here, because If I repeat the same experiment 1000 times and plot a histogram, I get a normal distribution curve. Is the central theorem useful in my case? In the definitions I found, to be able to compute an estimated mean with a certain error, one need to know the variance before hand and I don't know it.

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 This is more ore less textbook stuff. The key word here is t-statistic. Central limit theorem is certainly useful, if your latency has finite variance. If it does not, then it becomes trickier. – mpiktas Nov 22 '12 at 13:28

Perhaps you can bound your variance. Suppose, for example, that you know your data must be in the range [a,b]. Then Popoviciu's inequality bounds your variance by $\sigma^2 <= (1/4)(b-a)^2$. Using the upper bound in the formulas you found will be a bit of overkill, but it should satisfy your requirements.

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CTL is all about independent and identically distributed (i.i.d.) random variables, with finite mean and variance. I edit the answer just to add that you don't have to know your parameter , but be sure that this parameter is finite and identical along your runs.

In order to estimate the parameter mean with unknownk variance you can build an interval using the t-student as

where t is the value of a t-student with n-1 degrees of freedom with 1-a confidence level.

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Do you have any pointer on how to calculate the number of experiment to have 95 accuracy without knowing the variance? thanks – Djellel Eddine Nov 22 '12 at 13:16
-1, Answers should be answers, this is more like an unfinished comment. Please elaborate more. – mpiktas Nov 22 '12 at 13:31