Final answer:
A bar chart is the most effective graphic to display the number of students attending each of the state's public universities because it clearly represents categorical data with numerical values.
Step-by-step explanation:
In determining the most effective graphical representation for showing the number of last year's high school graduates attending each of the state's 19 public universities, a bar chart would be most effective. A bar chart excels in presenting categorical data with counts or numbers attached to each category, in this case, the number of students attending each university. In comparison, a pie chart is generally better for showing proportions of a whole at a single point in time, a line graph for showing data points over a continuous time interval, and a scatter plot for displaying the relationship between two quantitative variables.