One of the best ways to explore and try to understand a large dataset is with visualization. Place the numbers into a visual space and let your brain or your readers’ brain find the patterns. We’re good at that. You can often find stories that you might never have found with just formal statistical methods.
John Tukey, my favorite statistician and the father of exploratory data analysis, was well versed in statistical methods and properties but believed that graphical techniques also had a place. He was a strong believer in discovering the unexpected through pictures. You can find out a lot about data just by visualizing it, and a lot of the time this is all you need to make an informed decision or to tell a story.