Question

What would a wide box on a box plot tell you about your data? How about a narrow box?

Answer 1

Nothing. It has no relationship to the data.

Explanation:

The "width" of a box in a box plot chart has no significance to the data. It is simply an adjustment of the chart size to the number of items displayed.
The critical parameters of a box plot are the LENGTH of the box and the length of the "whiskers" extending up and down from the box.

NOTE: Some plots may place the boxes horizontally instead of vertically. In THAT case the "width" and "length" roles are reversed. Normally, box plots are displayed vertically.

http://www.purplemath.com/modules/boxwhisk.htm