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%