11.2.1 Mean, Standard Deviation, and Variance

(`mean``x`)-
Arithmetic mean (
*sample mean*) of`x`:(11.1)

(`variance``x`)-
Estimated (
*sample*) variance of`x`:(11.2)

This function computes the mean via a call to`mean`. If you have already computed the mean then you can pass it directly to`variance_m`.

(`variance_m``x, mean`)-
Estimated (
*sample*) variance of`x`relative to`mean`:(11.3)

(`sd``x`)

(`sd_m``x, mean`)-
The standard deviation is defined as the square root of the variance of
`x`. These functions returns the square root of the respective variance-functions above.

(`variance_with_fixed_mean``x, mean`)-
Compute an unbiased estimate of the variance of
`x`when the population mean`mean`of the underlying distribution is known*a priori*. In this case the estimator for the variance uses the factor and the sample mean is replaced by the known population mean :(11.4)