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