Under most conditions, as the sample size gets sufficiently large (technically as $n$ approaches infinity), the mean and variance of the sample data will approach the true mean and variance of the population.
Formally, if $X_1, X_2, X_3, \dots, X_n$ is a sequence of [[independent and identically distributed|iid]] random variables from any distribution with mean $\mu$ and variance $\sigma^2 < \infty$, then
$\bar X_n \overset{P}{\to} \mu$
This is to say that the sample mean $\bar X$ [[converges in probability]] to $\mu$ in the limit as $n$ goes to infinity.
The proof of the Weak Law of Large Numbers relies on
- [[Chebyshev's inequality]]
- the fact that $\bar X$ is an asymptotically unbiased estimator of the mean $\mu$
- that $\sigma^2 < \infty$
- the fact that $V(\bar X) \to 0$