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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 ChartsWhich 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. ReturnsAre 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 comparisonsbut 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