User:Oddtoddnm/Sandbox

Formulas

Standard Deviation

$\sigma =\frac{\mathrm{\Sigma }{(x-\mu )}^2}{N}$

$S=\frac{\mathrm{\Sigma }{(x-\overline{x})}^2}{N-1}$

Z Scores

$Z=\frac{x-\mu }{\sigma }$

$Z=\frac{x-\overline{x}}{S}$

Z Scores for Means

$Z_{\overline{x}}=\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{N}}}=\frac{\sqrt{N}(\overline{x}-\mu )}{\sigma }$