Central Limit Theorem (Topic 14 in Statistics)

[feranmidere]

The central limit theorem is described in the section for P-values in Statistics, the description could be used earlier instead of having a blank topic.

Markdown:
Central Limit Theorem

The theorem states that the mean of the sampling distribution of the sample means is equal to the population mean irrespective if the distribution of population where sample size is greater than 30.

And

The sampling distribution of sampling mean will also follow the normal distribution.

So, it states, if we pick several samples from a distribution with the size above 30, and pick the static sample means and use the sample means to create a distribution, the mean of the newly created sampling distribution is equal to the original population mean.

According to the theorem, if we draw samples of size N, from a population with population mean μ and population standard deviation σ, the condition stands:

i.e, mean of the distribution of sample means is equal to the sample means.

The standard deviation of the sample means is give by: