Pie Doughnut Bar Thinking Critically about Graphing

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Pie? Doughnut? Bar?Thinking Critically about
Graphing

• Lynn Stallings
• Marj Economopoulos
• Kennesaw State University

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Have you wondered what all these graphing options
are in spreadsheets?

• Column
• Bar
• Line
• Pie
• XY (Scatter)
• Area
• Doughnut

• Radar
• Surface
• Bubble
• Stock
• Cylinder
• Cone
• Pyramid

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Lets Talk About

• Standards What should we teach about graphing?
• Common Graphs - Bar, Line, Area, Pie
• Less Common Graphs Doughnut, Radar, Bubbles
• Appropriate, Inappropriate, and Misleading Graphs
  (Good, Bad, and Ugly)
• What makes a good graph?

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NCTM PSSM on Graphing

• In grades 6-8 all students should
• Select, create, and use appropriate graphical
  representation of data, including histograms, box
  plots, and scatter plots
• Discuss and understand the correspondence between
  data sets and their graphical representations,
  especially histograms, stem-and-leaf plots, box
  plots, and scatterplots.
• Make conjectures about possible relationships
  between two characteristics of a sample on the
  basis of scatterplots of the data and approximate
  lines of fit.

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What does the American Statistical Association
say?

• The American Statistical Association set up a
  group to write Guidelines for Assessment and
  Instruction in Statistics Education (GAISE).
• Georgia connections on the PreK-12 author team
• Christine Franklin, Department of Statistics,
  University of Georgia
• Denise Mewborn, Department of Mathematics and
  Science Education, University of Georgia
• Landy Godbolt, The Westminster Schools
• For the Curriculum Framework developed by this
  group, see http//www.amstat.org/education/gaise/.

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What about the Georgia Performance Standards?
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The GPS mention some graphs that you teach, but
may not have studied in school . . .

• Both of the following were created by John
  Tukey, a Princeton statistician. His 1977 book
  Exploratory Data Analysis made them popular. Both
  are commonly taught in middle school mathematics.
• Box-and-whisker
• Stem-and-leaf

At least, not if youre my age.
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Bar, Line, Area

• Which to use when?
• Vertical vs. horizontal
• Does it matter?
• A population example

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Do you feel crowded?
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Does this make sense?
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Pie ChartsWhich do you prefer?
http//us.mms.com/us/about/products/milkchocolate/
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What about this pie chart?
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Which gives you a better picture of the percent
of each color you would find in a bag of MMs?
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Pie Charts

• Require proportional reasoning.
• Display data as a percentage of the whole.
• Are visually appealing.
• Dont communicate exact numerical data.
• Make it hard to compare two data sets.
• Are usually best for 3-7 categories.
• Should be used with discrete data.

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Lets look at a few of the unusual graphing
options in spreadsheets.

• Column
• Bar
• Line
• Pie
• XY (Scatter)
• Area
• Doughnut

• Radar
• Surface
• Bubble
• Stock
• Cylinder
• Cone
• Pyramid

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Doughnuts?
A doughnut graph shows how the percentage of each
data item contributes to a total percentage. Its
a pie chart with a hole.
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Radar Graphs
When you create a Radar chart you have a separate
axis for each category of data. It basically has
the appearance of spokes on a bike tire. When
does it help to see data arranged this way? What
about this example?
http//www.learning-styles-online.com/
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Bubble Charts

• A bubble chart is basically just an XY (scatter)
  chart with an additional data series that is
  represented by the area of the point. In this
  example, the area of the point is the school
  systems enrollment (2005).

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Big enough to see . . .
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More on Bar, Line, Area

• Which to use when?
• Vertical vs horizontal
• Horizontal axis (vertical bars) time/continuous
• Possible discrete (categories possible)
• Vertical axis (horizontal bars) better for
  categories

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Category Data
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Same data horizontal bars
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Ordered horizontal bars
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A Drink called Cocaine
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A Sixth Grade Text

• Introduction to graphs
• Misleading graphs
• Role of scale, equal intervals
• Begin comparisons at zero line

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Stock market
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Growth vs. ReturnsAre these appropriate?
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Some common errors . . .

• The ratio of the heights of bars within each
  category does not reflect the actual ratio.
• There is an implied precision that is
  unrealistic.
• The percentages are computed incorrectly. A
  doubling of costs is only a 100 increase.

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Two groups comparison Questionnaire Statements ???
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Huh?
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Too many comparisonsbut global trends
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Whats wrong here?

• The 3-D effects make it difficult to read the
  bars.
• The non-horizontal scale artificially increases
  the lower-income bars compared to the
  upper-income bars.
• Some of the bars are missing a percentage.
• The interval sizes change. For example, all but
  the last two use 10,000.

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Is this appropriate?
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Whats wrong here?

• It is not clear from the horizontal axis where
  1980 starts and ends.
• The 3-D tilting makes the back lines look steeper
  even if they have the same slope.
• Do you think that workforce participation rates
  have been falling for women? Hint - look at the
  scale.
• It is nice picture of a bus and a bus-stop. Are
  they relevant?

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Women gt 25
50
Women 15-24
60
70
Men 15-24
80
Men gt 25
83
81
82
80
79
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Is this Better?
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Correct? Appropriate? Preferred?

• Is a certain choice of graph ever wrong for a set
  of data?
• Is so, what is an example?
• Are there times where you may make a choice among
  several types of graphs?
• If so, what criteria should you use?
• To think about . . .
• Excellence in statistical graphics consists of
  complex data communicated with clarity,
  precision, and efficiency. (Tufte)

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What are the characteristics of excellent
displays of data?

• Graphical displays should
• Show the data
• Induce the viewer to think about the substance
• Avoid data distortion
• Present many numbers efficiently
• Make large data sets coherent
• Encourage the eye to compare different pieces of
  data
• Reveal the data at several levels of detail
• Serve a reasonable, clear purpose
• Be closely integrated with statistical and verbal
  descriptions of the data

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Resources

• Examples of bad graphs http//www.stat.sfu.ca/cs
  chwarz/Stat-201/Handouts/node8.html
• http//www.shodor.org/interactivate/activities/
  and then select STATISTICS
• Huff, D. (1982). How to lie with statistics.
  Norton.
• Tufte, Edward R. (2006) The Visual Display of
  Quantitative Information. Graphics Press.

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Thank you!Have a great conference!

• Lynn, lstalling_at_kennesaw.edu
• Marj, meconomo_at_kennesaw.edu
• PowerPoint will be at http//ksuweb.kennesaw.edu/
  lstallin