standard error/ s. deviation

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standard error/ s. deviation
Message posted by J.T. on April 5, 2000 at 12:00 AM (ET)

Can someone please explain to me why the standard error of the sampling distribution is always smaller than the standard deviation of the population?

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Re: standard error/ s. deviation
Message posted by Phil Rosenkrantz on April 6, 2000 at 12:00 AM (ET)

The standard error is the standard deviation divided by the square root of the sample size. Mathematically, the standard error will always come out smaller when the sample size is greater than one.

Logically, this makes sense also. This is because if you take a sample from a population, it is likely to have some low, middle, and high values in it that will average out closer to the mean than if you just looked at one unit randomly drawn from the population. So the sample average has less dispersion...more of a tendency to been closer to the mean.

Hope that helped a little.

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