Statistics Notes

Mean
\bar{x}=\frac{\sum x_{i}}{n}
Sample Variance
s^{2}=\frac{\sum \left( x_{i}- \bar{x} \right)^{2}}{n-1}
Population Variance
\sigma^{2}=\frac{\sum \left( x_{i}- \mu \right)^{2}}{n}
Sample Standard Deviation
s= \sqrt{ \frac{\sum \left( x_{i}- \bar{x} \right)^{2}}{n-1}}
Population Standard Deviation
\sigma= \sqrt{ \frac{\sum \left( x_{i}- \mu \right)^{2}}{n}}
Range
Range = highest value - lowest value
Regression
r= \frac{n\left(\sum{xy} \right)-\left(\sum{x} \right) \left(\sum{y} \right)}{ \sqrt{ \left[ n \left( \sum{x^{2}} \right)-\left( \sum{x} \right)^{2} \right]\left[ n \left( \sum{y^{2}} \right)-\left( \sum{y} \right)^{2} \right] }}
Line of best fit
y = a + bx