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I am trying to calculate the variance of $s^2=\frac{1}{n-1}\sum (x_i-\bar x)^2$. So what I want to find is $ Var(s^2)$.

I have seen different posts, but many of them seem to make the assumption that the population is normally distributed. I don't know anything about the distribution.

Can anyone help or guide me in the right direction?

chri344v
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  • You can find the general formula in many questions: here or here for example. – COOLSerdash Apr 04 '22 at 15:12
  • Thx! I have seen the first example before, and that is also what the second is referencing. I don't quite seem to understand it though. Especially the first part where he rewrites. – chri344v Apr 04 '22 at 15:49

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The variance of s^2 if the population is non-Normal in case of simple random sampling, is

       Var(s^2) = (1 / n)[μ4 - μ2^2(n - 3) / (n -1)]

If the population is Normal, then μ4 = 3σ^4, and μ2^2 = σ4. So, we get

                  Var(s^2) = 2σ^4 / (n - 1)
Amit Kumar
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