Introduction to Probability

Multivariable Calculus

Algorithms: Part II

Algorithms: Part I

Introduction to Software Design and Architecture

Calculus Two: Sequences and Series

LAFF Linear Algebra

Stanford Machine Learning

Calculus One

Computational Thinking

Effective Thinking Through Mathematics

CS50 Introduction to Computer Science


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] σ=1Ni=1N(xiμ)2\displaystyle\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2}, μ\mu is the average of x.
  • The “Sample Standard Deviation”: [unbiased] σ=1N1i=1N(xiμ)2\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(ee) And Logarithms(ln()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
  • week-3-exponents-and-logarithms
  • ee : is defined to be the rate of growth if we continually compound 100% return on smaller and smaller time periods: e=limo(1+1n)n2.718e = \displaystyle\lim_{o \to \infty}(1+\frac{1}{n})^{n} \approx 2.718, growth=ert;(r:rate,t:time)growth = e^{rt}; (r: rate, t:time)
  • An Intuitive Guide To Exponential Functions & e
  • Demystifying the Natural Logarithm (ln)