User:Oddtoddnm/Sandbox

Standard Deviation

${\displaystyle \sigma ={{\Sigma \left(x-\mu \right)^{2}} \over N}}$

${\displaystyle S={{\Sigma \left(x-{\bar {x}}\right)^{2}} \over {N-1}}}$

Z Scores

${\displaystyle Z={{x-\mu } \over \sigma }}$

${\displaystyle Z={{x-{\bar {x}}} \over S}}$

Z Scores for Means

${\displaystyle Z_{\bar {x}}={{{\bar {x}}-\mu } \over {\sigma \over {\sqrt {N}}}}={{{\sqrt {N}}\left({\bar {x}}-\mu \right)} \over \sigma }}$