Category:Standard Error

This category contains results about Standard Error.
Definitions specific to this category can be found in Definitions/Standard Error.

Let $S = \set {x_1, x_2, \ldots, x_n}$ be a random sample of size $n$ from a normal distribution $\Gaussian \lambda {\rho^2}$ whose mean is $\lambda$ and whose standard deviation is $\rho$.

Then the mean $m$ of $S$ has a normal distribution whose mean is $\lambda$ and a standard deviation is $\dfrac \rho {\sqrt n}$.

If $\rho$ is unknown, then $\dfrac \rho {\sqrt n}$ is estimated by $\dfrac s {\sqrt n}$, where:

$s^2 = \ds \sum_i \dfrac {\paren {x - m}^2} {n - 1}$

The value $\dfrac s {\sqrt n}$ is known as the standard error.