## 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:

## 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)