# Linear vs. Quadratic Change ​

One of the most common mistakes in chart design is to scale an area by two sides at the same time, producing a quadratic effect for a linear change. That overstates the larger numbers and produces a badly skewed chart. A little care and some basic high-school math can help avoid the problem.

The following detail from a information graphic produced by Princeton's International Networks Archive illustrates the problem (the numbers are presumably from 2002):

Comparing Starbucks (\$4.1bn) and KFC (\$8.2bn), the problem becomes clear: the difference is a factor of two, but the KFC logo has four times the area of the Starbucks logo (even more because one is square and the other round). This can be seen in a number of the graphics on that website, though they also have some where they scale correctly.

The reason for the problem here is the use of logos (or of images, more generally) to make charts look better. Scaling a logo in only one dimension (which would be done in a bar chart) does not work because the image would look stretched and ugly. So instead, the image is scaled in two dimensions, leading to a perceived difference that is the square of the actual difference.

In more general terms, a linear change (I will use a factor of two to illustrate this)