Under what conditions might the median be a preferable measure of center to use, rather than the mean?
When a dataset has a few very extreme cases.
Example: We have a dataset of 1000 in which most values hover around the 1000-mark. Let's say the mean and the median are both 1000. Now we add one 'millionaire'. The mean will rise dramatically to almost 2000, while the median will not really change, because it will be the value of case 501 in stead of the in-between of case 500 and case 501 (cases arranged in order of value)