Mean and Mean Deviation (MAD) Simulation
James P. Dildine, 2000

Description
This Java Applet (Model) displays the lengths of five measured line segments.

| A | B | C | D | E |

The last two line segments (Mean and MAD) are controlled by the other five measured segments.

The Mean segment is calculated as the arithmetic average of the 5 measured segments. The Mean is calcualted by measuring the length of each line and then averaging them.
Then the mean line segment is constructed to reflect this mean length.

The MAD (Mean Absolute Deviation or Mean Deviation) represents the measurements of the average of the absolute deviations of data points from their mean. It is a measure of the variability in a data set. Most of the time you want it to be small (less variation)

Simulation
Manipulate the line segments and take note of the influence that these manipulations have on the mean and subsequently on the MAD or Mean Deviation.
Activities
Some questions to consider as you manipulate the line segment measurments.

1. Manipulate the line segments What influence does this have on the mean and the MAD?

2. Mean and Mean Deviation (MAD):

What makes the MAD move toward zero?
How can you make the MAD greater than the mean?
When is the MAD less than the mean?
How can you make the mean and MAD equal?

3. Now, Manipulate OP, named "C". Watch the SUM |Xi - C| and the SUM (Xi - C)^2.

Watch each individual calculation for the least value.
Each of those lowest values means something.
The first SUM |Xi - C| makes C the Median.
The second SUM (Xi - C)^2 would make C the Mean.

Javascript Example

Try this table out.
Enter Xs in the First Column then CLICK Calculate

 X X - Mean | X - Mean | Sum: Mean: Mean Deviation:
or