Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?

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Mathematics

Larry Yu

13 May, 03:46

Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?

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Zachary Hebert · Answer 1

If the mean of the sample standard deviations is equal to the population standard deviation, then the sample standard deviations target the population standard deviation and are called an unbiased estimator.

If the mean of the sample standard deviations is not equal to the population standard deviation, then the sample standard deviations target the population standard deviation and are called a biased estimator.

A biased estimator regularly underestimates or overestimates the parameter.

An unbiased sample statistics are good estimators A biased sample statistics are not good estimators.