Does the central limit theorem apply to non-normally distributed variables? Why?
Dear, Zam Ham,
No because they are normal . If any questions ZAM HAM lemme know
Sorry Stacie. The central limit theorem does apply. Google central limit theorem.
Yes, the central limit theorem (CLT) does apply to non-normally distributed variables. However, it is important to note that the CLT only applies to sufficiently large sample sizes.
The central limit theorem states that the sampling distribution of the mean of a random sample will approximate a normal distribution, regardless of the shape of the population distribution, as the sample size increases.
To understand why, let's assume we have a population with any distribution shape, not necessarily normal. When we take random samples from this population and compute the sample means, the central limit theorem tells us that the distribution of these sample means will be approximately normal, regardless of the original population distribution.
This occurs because, as the sample size increases, the individual random observations tend to cancel each other out to some extent. The distribution of the sample means becomes less influenced by the shape of the original distribution and more concentrated around the true population mean.
The central limit theorem is a powerful concept that allows us to make inferences and perform hypothesis testing using the properties of the normal distribution, even when the underlying variables are not normally distributed. However, it is essential to remember that the CLT's assumptions, particularly the requirement of a sufficiently large sample size, must be met for the approximation to hold.