Tuesday, February 11, 2014

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!!

1 comment:

  1. Love this task! Susan Friel developed a version of it for CMP back in the day. In our writing of CMP3, she was gung ho for the "mean as a balance point" idea. I am less optimistic about the pedagogical uses of this idea. You have nicely captured my concern, I think—that the meaning of 'balance' is not cleanly applied to data sets.

    Now to answer your question: If it caught your eye, I am guessing it is because she wrote (1) while you had (2) in mind. I know I tend to pay more attention to answers that violate my expectations (and, of course, I learn more from them too).