What are two commonly used graphs to display the distribution of a sample of categorical dat?

Ineed i been stuck on this question since yesterday

These box plots show the number of electoral votes one by democratic and republican presidential candidates for the elections from 1984 through 2012. which statement best compares the spread of the data sets

Aclassmate thinks that solving a system by graphing gives an exact answer when the lines appear to cross at a grid point, but only an approximate answer when they don't. explain why this isn't true.