3.5 Absolute Differences Simulation

This section is an interactive demonstration. The live simulation runs on the original site: open the demonstration at onlinestatbook.com.

Learning Objectives

1. Understand what it means to minimize the sum of absolute deviations
2. Learn which measure of central tendency minimizes the sum of absolute deviations.

Instructions
This demonstration allows you to examine the sum of absolute deviations from a given value. The graph to the right shows the numbers 1, 2, 3, 4, and 5 and their deviations from an arbitrary starting value of 0.254 shown by the black bar (the figure displays this rounded to 0.25).

The first number, 1, is represented by a red dot. The deviation from 0.254 is represented by a red line from the red dot to the black line. The value of the black line is 0.254. Similarly, the number 2 is represented by a blue dot and its deviation from 0.254 is represented by the length of a blue line.

The portion of the graph with the colored rectangles shows the sum of the absolute deviations. The sum of the deviations is equal to 0.746 + 1.746 + 2.746 + 3.746 + 4.746 = 13.73 as shown by the height of the colored bar.

In this demonstration, you can see the effect of moving the black bar.

Slide Show

Adapted from Online Statistics Education: A Multimedia Course of Study (onlinestatbook.com), Project Leader: David M. Lane, Rice University. Developed with NSF support. The original work is in the public domain; it is cited here at the authors' request. Changes were made: reformatted as an accessible XYZ web edition with native MathML. License: Public-Domain.