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Updated: Sep 14 2019

Statistical Distributions

  • Descriptive Statistics
    • Mean
      • Average of all observation
      • Mean = (sum of all observations)/(sample size)
    • Median
      • The middle value of all observations
      • If sample size is odd
        • Median = ((n+1)/2)th largest value
      • If the sample size is even
        • Median = the average of the (n/2)th and ((n/2)+1)th largest value
    • Mode
      • The most commonly occurring value
      • If there is more than one most commonly occurring value, there are as many modes as most commonly occurring values
  • Types of Distributions
    • Normal
      • aka Gaussian, bell-shaped
      • Mean = median = mode
    • Bi-modal
      • Distribution has two humps (each being a relative mode)
      • If symmetrical, mean = median
    • Skewed
      • Positive Skew
        • Asymmetrical with tail trailing off to right 
        • Mean > median > model
      • Negative Skew
        • Asymmetrical with tail trailing off to left
        • Mean < median < mode
      • Mean very sensitive to skew
      • Median somewhat resistant to skew
      • Mode very resistant to skew
  • Characteristics of the Normal Distribution
    • Defined entirely by two parameters
    • Mean (µ)
      • Standard deviation (σ)
    • A certain percentage of all observations will always fall within +/- certain standard deviations of the mean
      • +/- 1 Standard deviation = 68%
      • +/- 2 Standard deviations = 95%
      • +/- 3 Standard deviations = 99.7%
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