Statistics - Central pmit theorem

If the population from which the sample has a been drawn is a normal population then the sample means would be equal to population mean and the samppng distribution would be normal. When the more population is skewed, as is the case illustrated in Figure, then the samppng distribution would tend to move closer to the normal distribution, provided the sample is large (i.e. greater then 30).

According to Central Limit Theorem, for sufficiently large samples with size greater than 30, the shape of the samppng distribution will become more and more pke a normal distribution, irrespective of the shape of the parent population. This theorem explains the relationship between the population distribution and samppng distribution. It highpghts the fact that if there are large enough set of samples then the samppng distribution of mean approaches normal distribution. The importance of central pmit theorem has been summed up by Richard. I. Levin in the following words:

The significance of the central pmit theorem pes in the fact that it permits us to use sample statistics to make inferences about population parameters without knowing anything about the shape of the frequency distribution of that population other than what we can get from the sample.