Question

according to the central limit theorem (clt), no matter which distribution the data is collected from, as long as some conditions are met, we can always expect the sample average to behave like a normal random variable, i.e., the sampling distribution can be approximated by a normal distribution. which is not a clt condition for sample mean?

Answer 1

The Central Limit Theorem (CLT) is a fundamental concept in statistics, and it states that the distribution of the sum (or average) of a large number of independent, identically distributed random variables will be approximately normal, regardless of the original distribution of the variables, under certain conditions.

What is it about?

The random variables should be drawn from the same probability distribution. For the CLT to hold, the sample size should be sufficiently large.

There is no strict rule for what constitutes "large enough," but a commonly used guideline is that a sample size of 30 or greater is often sufficient. However, the larger the sample size, the better the approximation to a normal distribution.