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==Explanation==
 
==Explanation==
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{{w|Pie_chart|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 that bends out of plane in order to fit a 30% larger area into the footprint of a circle.
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{{incomplete|Created by ''a cosmologist discussing the unusual curvature of space in the area'' - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
  
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This shape does not aid in understanding the figures. At best, it serves to highlight a methodical error. Pie charts are intended to represent nonoverlapping fractions of a whole. If the entire pie does not represent the whole, and each sector a disjoint piece, then the pie chart is misleading and may be impossible to draw. A different type of chart should be used.
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{{w|Pie_chart|Pie Charts}} graph quantities 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.
  
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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 [[wikipedia:approval voting|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. For instance, for 2 colors, Red and Green, the pie chart could have four sectors: approval of both R and G, of just R, of just G, and of neither R nor G. These will necessarily add to 100%, since they exhaust all logical possibilities. If this is impossible or confusing, a completely different representation should be used, such as a bar chart.  An exception can occur if the percentages of the pieces have been rounded for readability—the percentages do indeed sum to 100, but after they are each rounded individually, the rounded numbers can sum to a slightly different value. This is still appropriate for a pie chart, and when charts like this are published, a small notice is sometimes published beneath it explaining the discrepancy due to rounding. If each group is rounded to the nearest 1%, with 0.5 rounded up, then the maximum possible sum of rounded percentages is (100+⌊n/2⌋)%, where n is the number of groups and ⌊•⌋ is the floor function. For instance, with groups of size 0.5%, 0.5%, 0.5%, and 98.5%, they would round up to 1%, 1%, 1%, and 99%, for a sum of 102% = (100+4/2)%.
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The resulting warped circle is then actually part of a [[wikipedia:Hyperbolic geometry#Circles and disks|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.)
  
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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.
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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 [[wikipedia:approval voting|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%.
  
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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.
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Percentages don't ''need'' to add up to 100% to be correct. For example, if five people wear blue t-shirts and five 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 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.
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The title text presents an alternative if shading is not possible, namely to excuse the percentage inaccuracy with scientists discussing curvature of space.
 
  
 
==Transcript==
 
==Transcript==
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:[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.]
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{{incomplete transcript|Do NOT delete this tag too soon.}}
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:[Two colored circles are shown. The circle on the right is fuzzy 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.]
  
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:[The left pie chart:]
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:[The left circle:]
 
:Wrong:
 
:Wrong:
 
:45% (red)
 
:45% (red)
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:40% (green)
 
:40% (green)
  
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:[The right warped and bent pie chart with shadows:]
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:[The right fuzzy circle with shadows:]
 
:Right:
 
:Right:
 
:45% (red)
 
:45% (red)
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{{comic discussion}}
 
{{comic discussion}}
  
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[[Category:Cosmology]] <!-- title text -->
 
 
[[Category:Pie charts]]
 
[[Category:Pie charts]]
 
[[Category:Comics with color]]
 
[[Category:Comics with color]]

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