Law of Large Numbers, brief explaination

What is law of large numbers?

In very simpler words, law of large numbers says that if we have large enough data — the average of the data — is same as expected value of the data.

More technically, law of large numbers states that —

As we collect and get large enough data on a random variable (x), the mean converges to the expected value.

mean of x=(x1 + x2 + .. xN) / N → expected mean, where N → ∞

Emphasis on large enough here. What large enough is depends on expected distribution as well. The speed on convergence — might be different.