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# How does a sample size impact the standard deviation?

If I take 10 items (a small sample) from a population and calculate the standard deviation, then I take 100 items (larger sample), and calculate the standard deviation, how will my statistics change?

The smaller sample could have a higher, lower or about equal the standard deviation of the larger sample. It's also possible that the smaller sample could be, by chance, closer to the standard deviation of the population. However, A properly taken larger sample will, in general, be a more reliable estimate of the standard deviation of the population than a smaller one.

There are mathematical equations to show this, that in the long run, larger samples provide better estimates. This is generally but not always true.

If your population is changing as you are collecting data, then a very large sample may not be representative as it takes time to collect. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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