Comparing mean and median measures of central tendency

Mean and median 1.How to calculate the mean and median 2.Geometric interpretation 3.What they tell us about the data

Procedure: add values and divide by number of values x = [4, 1, -2, 2, 0] x = (4 + 1 – )/5 = 1 Fancy formula: data: Mean aka “average” or “arithmetic mean” average: Example:

x = [4, 1, -2, 2, 0] x = (4 + 1 – )/5 = 1 Geometric interpretation of mean Example: The mean is the balance point (or center of mass) if points are weighted by distance to balance point

Procedure: sort values and take one in middle position x = [4, 1, -2, 2, 0] Median median Example:[-2 0, 1, 2, 4] reorder For an even number of values – take average of middle two x = [4, 1, -2, 2, 0, 2] median: Example:[-2 0, 1, 2, 2, 4] reorder (1 + 2 )/2 = 1.5

x = [4, 1, -2, 2, 0] Geometric interpretation of median Example: The median is the balance point (or center of mass) if points each have a weight of median [-2 0, 1, 2, 4] reorder

x = [100, 1, -2, 2, 0] x = ( – )/5 = 20.2 What happens for outliers? Example: The outlier changes the mean but not the median median is still one x = [4, 1, -2, 2, 0]