User:Oddtoddnm/Sandbox

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

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

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

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

Z Scores for Means
$$Z_\bar{x} = {{\bar{x} - \mu} \over {\sigma \over \sqrt{N}}} = {{\sqrt{N} \left ( \bar{x}-\mu \right )} \over \sigma}$$