# Mean Absolute Deviation Exploration

- Author:
- Kathryn Shafer

- Topic:
- Statistics

The applet shows five movable points, the mean and the Mean Absolute Deviation (MAD). The segments show the distance from the mean for each point. This is also called the deviation.

- Drag the points left and right. Write down what you notice about the mean and MAD and discuss with a classmate.
- Drag the points to meet the requirements listed below. If possible, see if you can find more than one way to position the points.
- The mean is 10, the MAD is 4, and no points are on the mean.
- The mean is 8, the MAD is 8, and no points are on the mean.
- The mean is 10, the MAD is 4, and exactly one point is on the mean.
- The mean is -2 and the MAD is 3, and no points are on the mean.
- Discuss the strategies you used in #2.
- Place the points such that the mean is 0 and the MAD is 4. Make a conjecture about the relationship between the points, the line segments, and the MAD.
- Create a challenge problem for your classmates.