The Central Limit Theorem describes the characteristics of the "population of the means" which has been created from the means of an infinite number of random population samples of size (N), all of them drawn from a given "parent population". The Central Limit Theorem predicts that regardless of the distribution of the parent population:
[1] The mean of the population of means is always equal to the mean of the parent population from which the population samples were drawn.
[2] The standard deviation of the population of means is always equal to the standard deviation of the parent population divided by the square root of the sample size (N).
[3] [And the most amazing part!!] The distribution of means will increasingly approximate a normal distribution as the size N of samples increases.
Cited from http://www.chem.uoa.gr/applets/appletcentrallimit/appl_centrallimit2.html
The law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
Cited from http://en.wikipedia.org/wiki/Law_of_large_numbers
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