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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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