In this case, the table is from The College Board, showing changes in the percentage of in-state freshmen in our nation's public universities. You can see the raw data by downloading Table 28, here. What you can't see by looking at that table, of course, is the overall pattern. That's where a picture comes in.
There are only two numeric values in the table: Percentage of freshman enrollment that are state residents in 2002 and 2012. I added a third, by subtracting one from the other. Then I put them on a choropleth hex map, a format I like because all the states are the same size. On this map, orange colors show states where the percentage of in-state residents has increased; purple shows a decrease, and grays are mostly even.
Be careful about interpreting this data. This visualization does NOT show, of course, that a university system is enrolling fewer in-state students; in fact, the number could have gone up if non-resident enrollment also increased, but at a faster pace. It just shows what has happened to the makeup of that freshman enrollment: More in-state (orange) or less in-state (purple).
What do you see?