Standard Errors of Mean , Variance , and Standard Deviation Estimators H F G E t u s

by Sangtae Ahn, Jeffrey a Fessler
Concrete ()


We often estimate the mean, variance, or standard deviation from a sample of standard errors or error bars (in plots) as well. A standard error of a statistic (or estimator) is the (estimated) standard deviation of the statistic. An error bar is, in a plot, a line which is centered at the estimate with length that is double the standard error. Standard errors mean the statistical fluctuation of estimators, and they are important particularly when one compares two estimates (for example, whether one quantity is higher than the other in a statistically meaningful way). In this note we review the standard errors of frequently used estimators of the mean, variance, and standard deviation.

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