## Sampling distribution

Sampling distribution refers to the probability distribution of a given statistic based on a random sample. It helps in determining the behavior of a statistic when sampled repeatedly.

For example, if we take multiple samples of a certain size from a population and calculate the mean of each sample, the sampling distribution of the sample means will show how the sample means vary around the population mean. This distribution will help in making inferences about the population mean based on the sample means.

Another example is the sampling distribution of the sample proportion. If we take multiple samples from a population and calculate the proportion of a certain characteristic in each sample, the sampling distribution of the sample proportions will show how the sample proportions vary around the population proportion.

- Inferential statistics heavily relies on the concept of sampling distribution to make predictions about population parameters based on sample statistics.
- The central limit theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

Sampling distribution is a crucial concept in statistics as it helps in making accurate inferences about a population based on sample data.

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