Central Limit Theorem states that the relationship between population variance and sample mean variance is $var(\bar{x})=\sigma^2/n$.
I'm trying to verify this with dataset (0,0,0,1,2,9) which has $\mu=2$ and $\sigma^2=10.33$ by conducting experiment with sample size of 2 with replacement $(x_1, x_2)$, and calculate the mean variance from all possible outcomes.
the result I got was:
$$var(\bar{x})=\frac{1}{36}\Sigma (\bar{x_i}-\mu)^2=\frac{186}{36}=5.17$$
$$5.17 \ne \frac{10.33}{36}=0.29$$
Could anyone help point out whether I get anything wrong in my calculation?