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Explanation of Neighborhood Example

Scenario 1: The "Upper Class" Neighborhood

So just how is it possible that one person can claim the average income in the neighborhood is $150,000 while another can claim it is only $35,000? Both are "honest" people who are using legitimate statistics, but they are using different definitions for "average." Lets look at the data in this neighborhood a little closer so that we can see just what is going on (hint: try changing the bin size on the histogram)...

Neighborhood Incomes
Garnett $1,000,000
Jackson $225,000
Nelson $80,000
Olson $60,000
Smith $40,000
Jones $30,000
Howard $20,000
Johnson $20,000
Hamlin $15,000
Pafko $10,000
----- -----
Mean $150,000
Median $35,000
Mode $20,000

The mean, median, and mode are so different because the income distribution is not symmetrical. The Garnett & Jackson households are quite wealthy. Therefor they greatly increase the mean income for the entire neighborhood (if they did not live here; the mean, median, and mode would be $34,375, $25,000, & $20,000 respectively). There are two lessons to be learned from this data:

  1. The word "average" is meaningless unless you know whether it refers to the "mean", "median", or "mode."
  2. A few outliers can greatly skew the summary statistics. The mean is usually more sensitive to outliers than the median or mode.

Note: The applet used to create the above histogram can be obtained from the Globally Accessible Statistical Procedures (GASP) web site. It was created by R. Webster West, Dept. of Statistics, Univ. of South Carolina west@stat.sc.edu


Copyright 2000, Wayne Pafko