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.

As you might have already notice the four datasets are Anscombe´s quartet, I just put them all together at the beginning. You can find the code to get the data and reproduce the plots here.