Mathematics: Statistics

Statistics Formulas

• Sample
  • Sample Mean:    $\bar{x} = \frac{\sum x_{i}}{n}$
  • Sample Variance:    $s^{2} = \frac {\sum(x_{i}-\bar{x})^2}{n-1}$
  • Sample std:    $s = \sqrt{s^{2}}$
  • Sample Covariance;    $cov = \frac{\sum(x-\bar{x})^2 (y-\bar{y})^2}{n-1}$

• Population
  • Population Mean:    $\mu = \frac {\sum(x_{i})^2}{N}$
  • Population Variance:    $\sigma^{2} = \frac {\sum(x_{i}-\mu)^2}{N}$
  • Population Std:    $\sigma = \sqrt{\sigma^{2}}$
  • Population Covariance:    $cov = \frac{\sum(x - \mu_{x})^2(y - \mu_{x})^2}{N}$

• Others
  • Correlation:    $p (X,Y) = \frac{Cov(X,Y)}{\sigma_{x}\sigma_{y}}$
  • Mean Absolute Deviation (MAD):    $MAD = \frac{\sum|X_{i}-\bar{X}|}{n}$