A Question of Balance

This post is based on a student comment that caught my eye while grading. The data below shows the sodium content (in mg) for 23 brands of "regular" Peanut Butter.

The student wrote one of the following two statements in defense of choosing the preferred measure of center.

1) The data are balanced on each side of the median.
2) The data are balanced on each side of the mean.

Which statement do you think is more correct? In what sense might someone think the other one is correct, too?

Ready... GO!!