Question

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?

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.