The lowest and greatest values in this data set are 15 and 32, which correctly match the left and right ends of the whiskers in the given plot. Furthermore, this data set can be divided into two sets of five numbers:

15, 16, 16, 16, 19 and 23, 23, 27, 29, 32

This shows that the median is $\displaystyle\frac{{{19}+{23}}}{{2}}={21}\usepackage{cmbright}\Huge\$ , which matches the line in the middle of the box. The median of the lower set is 16; the median of the upper set is 27. These numbers match the left and right ends of the box, respectively.