How is the 5-number summary used in constucting a boxplot?
The 5-number summary gives you the points on the boxplot.
First you put your cases in order of value/score.
Minimum (MIN) -- lowest value
First Quartile (Q1) -- the value when you reach 25% of your cases.
Median (MED or Q2) -- the value of the middle case
Third Quartile (Q3) -- when you are at 75% of your cases
Maximum (MAX) -- highest value
The 'Box' thus has 50% of all cases.
The picture is in Dutch (Wikipedia), but it should be clear. At the right side it makes the distinction between "largest non-extreme" (the line) and the maximum (the x). Because sometimes it is more realistic to leave some of the extremes out of the picture.