Define: Central Limit Theorem

The Central Limit Theorem states that when independent random variables are added, their sum tends to follow a normal distribution, regardless of the shape of the original variables’ distribution.

The Central Limit Theorem is important because it allows us to make inferences about a population based on a sample. It provides a foundation for statistical hypothesis testing and confidence interval estimation.

The Central Limit Theorem applies to any type of data as long as the sample size is sufficiently large. However, it is most commonly used for data that follows a bell-shaped distribution.

There is no fixed rule for the minimum sample size required for the Central Limit Theorem to apply. However, a general guideline is that the sample size should be at least 30 for the theorem to hold reasonably well.

The Central Limit Theorem assumes that the samples are randomly selected. If the samples are not randomly selected, the theorem may not hold, and alternative statistical methods may need to be used.

The Central Limit Theorem is most reliable for large sample sizes. For small sample sizes, the distribution of the sample mean may not perfectly follow a normal distribution, but it can still provide useful approximations.

The Central Limit Theorem is primarily used for numerical data. However, it can be extended to certain non-numerical data if appropriate transformations are applied to make the data numerical.

The Central Limit Theorem assumes that the random variables being added are independent and identically distributed. Violation of these assumptions can limit the applicability of the theorem.

The Central Limit Theorem is a fundamental concept in statistics and is widely applicable. However, its use may depend on the specific analysis being conducted and the underlying assumptions of the statistical model.