Pie Charts
Pie Charts
[Two colored circles are shown. The circle on the right is warped and bent in shape and shows some shadows from the middle to the outer edges, like a round piece of cloth with wrinkles going out from the center.]
[The left pie chart:] Wrong: 45% (red) 15% (blue) 30% (yellow) 40% (green)
[The right warped and bent pie chart with shadows:] Right: 45% (red) 15% (blue) 30% (yellow) 40% (green)
[Caption below the frame:] How to make a pie chart if your percentages don't add up to 100

Pie Charts graph proportions as "slices" of a circle, like a pie that you cut into slices.  The circle, or Pie, represents the whole sum of the slices, or 100% of the data.  As such, if the data represented by the slices is expressed as percentages, the total of all the slices, by definition, must total 100%.  This comic introduces a new technique for getting around that rule by "warping" the circle to allow more than 100% of the data to exist in the graph. Thus the total amount of 130% is represented with a shape presumably 30% larger in area than the circle.
The resulting warped circle is then actually part of a hyperbolic plane , while a normal circle is part of a flat plane. Of course, it doesn't matter if the geometric shape is a circle or a hyperbolic plane: A changed graphic doesn't magically solve the misrepresentation of percentages. At best, it serves to highlight the methodical error. Regarding doctored statistics: If the same numbers were presented as absolute values instead of percentages, the error would still remain but would be less obvious, especially if you omit the total count of the sample ( Of all people asked, 40 selected green as favorite color, 45 selected red, 30 yellow and 15 blue. This statement omits that you surveyed only 100 people and several of them named several colors, and readers will assume a larger sample.)
Percentages that add up to more than 100% are often a sign that a math error has occurred, whether a typo somewhere or a sloppy case of taking numbers from different sources. However, they can arise naturally in cases where each item can belong to more than one group, such as approval voting (40% of the people like green 45% like red etc., however there may be some that like both green and red). In such cases, a more accurate depiction would have some form of overlap of the pie pieces, not a warping of the space which they occupy, or a completely different representation, such as a bar chart.  Minor cases can also occur if the percentages of the pieces have been rounded for readability - summing the rounded numbers can result in them adding to 99% or 101%.
Percentages don't need to add up to 100% to be correct. For example, if ten people wear blue t-shirts and ten wear red t-shirts, then 50% of them wear each color for a total of 100%. Now if one of each joins the group, 55% of the original population wears each color, for a total of 110%, as the total population risen by 10%. That said, this change should be represented by something like a bar graph, not by pie chart. If percentages are represented by a pie chart, the assumption is that the total should be 100%, independently of the math behind it.
In this case, the right image appears to be what happens when you cut the pie chart segments out of fabric, stitch them together, and let the resultant fabric flop around a bit.
The title text presents an alternative if shading is not possible, namely to excuse the percentage inaccuracy with scientists discussing curvature of space.
[Two colored circles are shown. The circle on the right is warped and bent in shape and shows some shadows from the middle to the outer edges, like a round piece of cloth with wrinkles going out from the center.]
[The left pie chart:] Wrong: 45% (red) 15% (blue) 30% (yellow) 40% (green)
[The right warped and bent pie chart with shadows:] Right: 45% (red) 15% (blue) 30% (yellow) 40% (green)
[Caption below the frame:] How to make a pie chart if your percentages don't add up to 100
