Graphics can show you in a faster way the characteristics of your data than a table or a summary statistic. But it also can show you more unexpected things.
I will show you this with the following example. Imagine you have a dataset with 44 points, the mean of x is 9, the mean of y is 7.5, the correlation between x and y is 0.816 and the linear regression line has an intercept of 3 and a slope of 0.5. Here is the plot :
Now we divide the original table of 44 points in 4 tables of 11 points. Each of these tables has the same mean of x and y, same correlation and same linear regression intercept and slope as the original table. I will plot it now and will use different colors for the 4 tables:
There seems to be different patterns for different categories. I will plot the 4 of them apart:
The characteristics of each table is quite different although the four of them have the same mean of x and y, the same correlation and the same interecept and slope for the linear regression, furthermore the 4 tables have the same variance of x and y. The information you get when you plot them by category is quite different that the information you get if you look at their simple summary statistics by category.