Central Limit Theorem (CLT) is the fundamental concept that allows researchers to make conclusions about a population, having drawn only a sample (inferential statistics).
When sufficient samples are drawn, the means of each sample form a normal, that is, a bell-shaped, distribution. This is called the sampling distribution.
The center of the sampling distribution is equal to the mean of the population (mu) from which the samples were drawn.
It's standard deviation is proportionate to the population's standard deviation, relative to the size of the samples (n). The smaller the sample size, the greater the variation, so, the wider the graph. Larger samples will produce a more narrow graph, that is, have smaller variation.
Samples are sufficent either when drawn from a normal population or are "sufficiently large." The common rule of thumb is for n >= 30.
