Standard Deviation #

• It is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
• The “Population Standard Deviation”: [biased] $\displaystyle\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2}$, $\mu$ is the average of x.
• The “Sample Standard Deviation”: [unbiased] $\displaystyle\sigma = \sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i - \mu)^2}$
• It’s an important change that to divide by N-1 (instead of N) when calculating a Sample Variance.
• Refers:
  • Wikipedia
  • MathisFUN

Exponents #

• Exponents($e$) And Logarithms($ln()$)
• Ask yourself this question: are we talking about inputs (cause of the change) or outputs (the actual change that happened?)
• Logarithms reveal the inputs that caused the growth
• Exponents find the final result of growth
• 
• $e$ : is defined to be the rate of growth if we continually compound 100% return on smaller and smaller time periods: $e = \displaystyle\lim_{o \to \infty}(1+\frac{1}{n})^{n} \approx 2.718$, $growth = e^{rt}; (r: rate, t:time)$
• An Intuitive Guide To Exponential Functions & e
• Demystifying the Natural Logarithm (ln)