How closely do sample means cluster around the population mean? The *standard deviation the distribution of all possible sample means for samples of size N*is called the “standard error of the mean” (or “standard error”). Recall from the Central Limit Theorem that the standard error, *s* _{x}, is equal to the population standard deviation, *s* _{x}, divided by the square root of the sample size, *N*:

Thus, for a sample of *N* = 25 and population standard deviation of* s* _{x} = 100, the standard error of the mean is 100/5 or **20**. For a sample of *N* = 100 and population standard deviation of* s* _{x} = 100, the standard error of the mean is 100/10 or **10**. Notice that when sample size *N* is increased, the standard error becomes smaller. In our example, by quadrupling the sample size, the standard error was cut in half.

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