# statistics

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How is the standard error of the mean influenced by sample size and standard deviation?

• statistics -

The standard error of the mean (SEM) is a measure of how well the sample mean is estimated - so if you increase the sample size, the standard error of the mean should get smaller. Specifically, if S is the standard deviation of the sample, then the SEM = S/sqrt(N), where N is the sample size. So you can also see from that that if the standard deviation of the sample increases, then the SEM increases proportionally with it.

• statistics -

Why does the standard of error of a mean decrease as population increases.

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