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Pie Doughnut Bar Thinking Critically about Graphing

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Pie Doughnut Bar Thinking Critically about Graphing

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    1. Pie? Doughnut? Bar? Thinking Critically about Graphing Lynn Stallings Marj Economopoulos Kennesaw State University

    2. Have you wondered what all these graphing options are in spreadsheets? Column Bar Line Pie XY (Scatter) Area Doughnut

    3. Let’s 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?

    4. 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.

    5. 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/.

    6. What about the Georgia Performance Standards?

    8. 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

    9. Bar, Line, Area Which to use when? Vertical vs. horizontal Does it matter? A population example

    10. Do you feel crowded?

    17. Does this make sense?

    18. Pie Charts Which do you prefer?

    19. What about this pie chart?

    20. Which gives you a better picture of the percent of each color you would find in a bag of M&Ms?

    21. Pie Charts Require proportional reasoning. Display data as a percentage of the whole. Are visually appealing. Don’t 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.

    22. Let’s look at a few of the unusual graphing options in spreadsheets. Column Bar Line Pie XY (Scatter) Area Doughnut

    23. Doughnuts?

    24. Radar Graphs

    25. 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 system’s enrollment (2005).

    29. 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

    30. Category Data

    31. Same data horizontal bars

    32. Ordered horizontal bars

    33. A Drink called Cocaine

    34. A Sixth Grade Text Introduction to graphs Misleading graphs Role of scale, equal intervals Begin comparisons at zero line

    36. Stock market

    37. Growth vs. Returns Are these appropriate?

    40. 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.

    41. Two groups comparison Questionnaire Statements ???

    42. Huh?

    43. Too many comparisons but global trends

    44. What’s 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.

    45. Is this appropriate?

    46. What’s 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?

    47. Is this Better?

    48. 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)

    49. 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

    50. Resources: Examples of bad graphs: http://www.stat.sfu.ca/~cschwarz/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.

    51. Thank you! Have a great conference! Lynn, lstalling@kennesaw.edu Marj, meconomo@kennesaw.edu PowerPoint will be at http://ksuweb.kennesaw.edu/~lstallin

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