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] σ = 1 N ∑ i = 1 N ( x i − μ ) 2 \displaystyle\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2} σ = N 1 i = 1 ∑ N ( x i − μ ) 2 μ \mu μ
The "Sample Standard Deviation ": [unbiased]σ = 1 N − 1 ∑ i = 1 N ( x i − μ ) 2 \displaystyle\sigma = \sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i - \mu)^2} σ = N − 1 1 i = 1 ∑ N ( x i − μ ) 2
It's an important change that to
divide by N-1 (instead of N) when calculating a Sample Variance.
Refers:
Exponents (e e e l n ( ) ln() l n ( ) 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 e e e defined to be the rate of growth if we continually compound 100% return on smaller and smaller time periods:e = lim o → ∞ ( 1 + 1 n ) n ≈ 2 . 7 1 8 e = \displaystyle\lim_{o \to \infty}(1+\frac{1}{n})^{n} \approx 2.718 e = o → ∞ lim ( 1 + n 1 ) n ≈ 2 . 7 1 8 g r o w t h = e r t ; ( r : r a t e , t : t i m e ) growth = e^{rt}; (r: rate, t:time) g r o w t h = e r t ; ( r : r a t e , t : t i m e ) An Intuitive Guide To Exponential Functions & e Demystifying the Natural Logarithm (ln)
