Graphing

Page 1

Spreadsheets, Calculators, and Graphing Lynn Stallings Marj Economopoulos Kennesaw State University




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


What about these graphing options in calculators?    

Scatter plot XY Line Histogram Box [and whisker] Plot with and without outliers  Normal Probability Plot (Shows if the distribution is normal.)


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?


A picture is worth ….  Expanded role of graphs & charts  New feature in Atlanta Journal & Constitution  Editorial page


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, stemand-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.


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).

 For the Curriculum Framework developed by this group, see http://www.amstat.org/education/gaise/.


Standards 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 you’re my age.


Histogram Frequency distribution

 An extension of stem & leaf  Tally marks in a chart format  Class interval depend on data


Using Excel to build histograms A data analysis tool in Excel

 Select data  Class intervals called “Bins”  Excel will calculate the frequencies  Need to know meaning for ranges  An example follows



The role of class intervals (bins)


Bar, Line, Area  Which to use when?  Vertical vs. horizontal  Does it matter?

 A population example


Do you feel crowded?


Years 20 06

19 90

19 70

19 50

19 30

19 10

18 90

18 70

18 50

18 30

18 10

17 90

Millions

US Population Column (Bar chart)

300

250

200

150

100

50

0


Years 2006

2000

1990

1980

1970

1960

1950

1940

1930

1920

1910

1900

1890

1880

1870

1860

1850

1840

1830

1820

1810

1800

1790

Millions

US Population Line

300

250

200

150

100

50

0


US Population Cylinder 300 250 200 Millions 150 100 50 0 1790

1820

1850

1880

1910 Years

1940

1970

2000


Does this make sense? US Population Pie

1 2 3 4 5 6 7 8 9 10 11 12 13 14


Pie Charts What communicates clearly? Plain M&M Color Distribution

brown yellow red blue orange green

http://us.mms.com/us/about/products/milkchocolate/


What about this pie chart? Plain M&M Color Distribution

brown yellow red blue orange green


Which gives you a better picture of the percent of each color you would find in a bag of M&Ms? Plain M&M Color Distribution

13%

16%

brown 14%

yellow red blue

20%

Plain M&M Color Distribution

13% 24%

brown yellow red blue orange green

orange green


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.


Let’s 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


Doughnuts? Demographics of Georgia (inner) and Atlanta Public School System (outer) Students 1%

8% 1%

4% Asian Black Hispanic Multiracial White

3% 38%

49% 2%

8% 86%

A doughnut graph shows how the percentage of each data item contributes to a total percentage. It’s a pie chart with a hole. It may be useful in comparing two groups, but represents them with unequal areas so may mislead.


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? This example is about learning styles. http://www.learning-styles-online.com/


Bubble Charts  A bubble chart is basically just an XY (scatter) chart that represents an additional data series in the area of the point. Selected Georgia School Systems 1000 900 Clinch, 1,317

800

Square Area

700 600 Chatham, 32,842

500

Gw innett, 143980

400

Forsyth Dade

Bibb

M us co g

Richmond

ee

Cobb

300 200

Fulton, 79192

Sumter Oglethorpe

Dekalb, 99544

Clayton

100 0 -200,000

0

200,000

400,000

600,000

County Population (2005)

800,000

1,000,000

1,200,000


Big enough to see . . . Selected Georgia School Systems

The area of the circle represents the school system’s enrollment.

1000 Ware, 6098 Burke, 4342

800

Sumter Oglethorpe

400

Fulton, 79192

Dade, 2449

Dekalb, 99544

M us

200

Bibb

Cobb, 105526

co ge

Richmond Forsyth

Gw innett, 143980

Chatham

e, 32 49 0

Sq. Area

600

Clayton, 51948

0 -200000

0

200000

400000

600000

-200

County Population (2005)

800000

1000000

1200000



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




Stock market


Growth vs. Returns Are these appropriate?



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.


Two groups comparison Questionnaire Statements ???


Huh?


Too many comparisons but global trends


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 upperincome bars.  Some of the bars are missing a percentage.  The interval sizes change. For example, all but the last two use $10,000.


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?

Women > 25

40% 50% 60%

Women 15-24

70% Men 15-24

80% ‘79

‘80

‘81

‘82

Men > 25

‘83


Is this Better?


Correct? Effective?  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)


Correct

Ineffective Clear

Incorrect


What are the characteristics of excellent displays of data? Graphical displays should

        

Show the data Encourage the viewer to think about the context 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


Resources:  Examples of bad graphs:    

http://www.stat.sfu.ca/~cschwarz/Stat-201/Handouts/ http://www.shodor.org/interactivate/activities/ and then select STATISTICS Huff, D. (1982). How to lie with statistics. Norton. Jones, G. E. (2000). How to lie with charts. Authors Choice Press. Tufte, Edward R. (2006) The Visual Display of Quantitative Information. Graphics Press.


Thank you! Enjoy the rest of your stay in Atlanta!  Lynn, lstalling@kennesaw.edu  Marj, meconomo@kennesaw.edu  PowerPoint will be at http://ksuweb.kennesaw.edu/~lstallin


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