The deficit is a problem. There’s no need to lie about it graphically

This article on the NPR Planet Money blog discusses the projected federal budget deficit as compared to the maximum deficit reduction discussed in recent debt-ceiling negotiations.

If we cut to the chase, there is a $9 trillion shortfall over the next ten years.  The most stringent deficit reduction measures discussed don't even come close to addressing the problem.

Compared to proposed spending cuts here, though, this is good progress.  At that point in the discussions, there was a $10.6 trillion shortfall!  (Here are some ways to visualize this huge number.)

Danger!  Misleading graphics ahead!

Each one of these posts has an accompanying graphic:  A large red circle with the amount of the projected federal budget deficit in it ($13 trillion) and a smaller green circle with the amount of the proposed reductions and cuts ($4 trillion or $2.4 trillion).  The problem with both of these graphics is that they suggest that the problem is bigger than it is — which, given the gigantic nature of the numbers, is completely unnecessary.

How are they misleading?  When marrying numbers to the relative size of graphics, size does matter, and the sizes are incorrect.  (There a little bit of math here, so be forewarned!)  Let's take the $2.4 trillion vs. $13 trillion graph.  I copied the graphic into Paint, and measured the diameters of the circles.  The green circle was 100 pixels across, and the red one was 298 pixels across.

To make a fair comparison between the size of two figures like this, the areas should be proportional.  This means that the red circle should have 13 / 2.4 = 5.42 times the area of the green circle.  Reaching deep into the recesses of middle school math class, we can figure out that the diameter of the red circle should be 233 pixels.  Something like this:

This is less than 298 pixels. The graphic isn't quite as dramatic, but it's true to the data. The same thing goes for the other graph.  The green circle was 123 pixels across, and the red one was 298 pixels across.  Running through the same argument, the diameter of the red circle should be 222 pixels:

So what happened?  One possibility might have been that the person designing the graphic just scaled the diameters by the ratio.  This would really have been misleading, but at least they would have taken a good shot at making the size of the graphics match quantitatively.  But this wasn't done.  It appears that the relative sizes of the circles in both graphs were just eyeballed.  There's nothing quantitative about the graphics at all, except that one number is bigger than the other.

Be careful when you're presented with a graphic like this.  You can be misled.