# Sampling and Sampling Distributions

Sampling involves selecting a subset of data from a population to estimate characteristics of the whole population.

## Sampling Distribution

The sampling distribution is the probability distribution of a statistic (such as the sample mean) obtained from a large number of samples drawn from a specific population.

WIP

## Central Limit Theorem

The central limit theorem states that the sampling distribution of the sample mean will approximate a normal distribution, regardless of the shape of the population distribution, provided the sample size is sufficiently large (usually $n = 30$).

$\bar{X} \sim \mathcal{N}(\mu, \frac{\sigma^2}{n})$WIP