Exercises

1. Note that the mean deviation from the mean and the mean deviation from the median are both zero. Change the data and see if this is still true.

2. Change the distribution so that it has a postive skew. Which is bigger, the mean or the median?

3. Change the distribution so that it has a negative skew. Now which is bigger, the mean or the median?

4. Investigate the relative size of the mean squred deviation from the mean and the mean squared deviation from the median. Which is smaller? When are they the same? Click here for a proof of your finding.

5. Although not shown in the applet, the median minimizes the mean absolute value of deviations. Click here for a proof.