Rolling a fair twelve- sided die produces a distribution set of numbers between 1 and 12 with a mean of 6.5 and a standard deviation of 3.452. Suppose that sample of n twelve sided dice are rolled many times and the mean of the outcomes is computed for each roll of n dice.
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The mean is the same for both samples: 6.5, but the SD is different: for n=36, SD=3.452/√36=3.452/6=0.5753 and for n=100=3.452/√100=3.452/10=0.3452. SD[sample]=SD[population]/√N where N is the sample size.

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