Let say how charts, graphs, figures, as well as tables, can save readers time and energy, aid their understanding of an article, and reduce the word count of the main text...
It is tempting to think of statistics, numbers, as the ultimate in conveying information, but that often is not true. Two examples immediately come to mind: (1) the p-value, and (2) r- and R-square. The first is meaningless as a stand-alone figure, and the second is often misinterpreted. Without a graph, you may not know what is driving that number. On the other hand, a scatterplot for a graphical residual analysis can be very meaningful, and often not so easily misunderstood.
Often, the best statistics quantify what you see in a graph. Consider a regression line where we use the estimated variance of the prediction error for each prediction to form prediction intervals to produce 'bands' about the regression line which would ideally encompass a given percent of the observations. A classic Shewhart control chart might be considered a somewhat similar example. "Numbers" and graphs can often be used well together.
Finally, an expression I like: "A picture is worth a thousand words." So many things can be seen in a graph, that a number of statistics may be used to describe the same information, and still fall short. If you want a number for an arbitrary threshold for a decision, then you might want to review your decision making process. I think that is commonly a fallacy in relying on a threshold for an hypothesis test. For example, one might test a regression for heteroscedasticity, but that may not provide a good decision or tell you what to do next. But if you estimate the degree of heteroscedasticity (using a coefficient of heteroscedasticity), you can learn what is the approximate impact. That same statistic-as-a-threshold thinking may minimize the importance of graphics, but they are important, not just for an exploratory analysis, but in the final analysis, and presentation of results.