Graphical Representation of Data

1
Unit 3

• Graphical Representation of Data

2
Ways the Graph Quantitative Data

• Stem-and-Leaf Plots
• Histograms
• Boxplots

3

• Exams Scores for 107 Students in a Statistics
  Course
• 60 70 69 59 75 54 59 79 63 83 75 63 68 82 76 70
  64 71 80 89 76 81 80 87 72 80
• 87 74 75 76 77 76 85 82 77 78 78 76 80 82 79 77
  76 79 88 74 81 85 91 74 89 84
• 89 82 78 85 82 87 86 86 91 81 84 80 85 86 82 86
  83 92 90 85 89 87 85 86 89 91
• 87 88 88 93 91 92 93 92 92 88 95 90 89 94 9 96
  90 90 94 94 92 94 96 97 96 94 95 91 95

4

• Stem-and -Leaf plot of the data
• Prototype "5 4" represents "54"
• 0 9
• 1
• 2
• 3
• 4
• 5 499
• 6 033489
• 7 0012444555666666777888999
• 8 00000111222222334455555566666777778888999999
• 9 0000111112222233444445556667

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What we learn from a stem-and-leaf plot

• Most common value (modal stem)
• Highest and lowest values
• Outliers
• Skewness

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Steps for creating a stem-and leaf plot

• Find the maximum and minimum values
• Decide on the digits for the stems and the leaves
  - aim for between 7 and 14 stems
• Create the trunk
• Write a prototype
• Round if necessary and place each leaf on the
  appropriate stem
• Reorder the leaves

7
Interactive to round and create stem-and-leaf
graph

• Exam scores of 16 students
• 94.64 91.23 94.75 93.56
• 96.19 86.61 79.54 72.13
• 87.26 63.18 78.59 59.04
• 53.55 74.93 58.88 60.38
• A-5 Basics Basics 2 (rounding and creating a
  stem-and-leaf graph)

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Interactive to round and create stem-and-leaf
graph

• Diameter in miles of the nine planets
• 1423.0 30200.0 31600.0 88803.0
• 4215.0 7921.0 7517.0 3030.0
• 74520.0
• A-5 Basics Basics 2 (rounding and creating a
  stem-and-leaf graph)

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From Stem-and-Leaf to Histogram

• A histogram is a stem-and-leaf graph rotated so
  that the trunk becomes the horizontal axis.
  Recall the stem-and-leaf graph for the 107 exam
  scores

10
Remember this basic shape and now rotate the
graph 90 degrees counterclockwise

• 0 9
• 1
• 2
• 3
• 4
• 5 499
• 6 033489
• 7 0012444555666666777888999
• 8 00000111222222334455555566666777778888999999
• 9 0000111112222233444445556667

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Histogram for the Exam Scores
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Interactive for stem-and-leaf vs histogram

• Data for the number of stories of 22 buildings in
  Chicago
• Creating both a stem-and-leaf graph as well as a
  historam
• A-5 Basics Practice 3

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Histograms vs stem-and-leaf graphs

• Notice the histogram has the same basic shape as
  the stem-and-leaf graph.
• Occasionally a stem-and-leaf graph contains so
  few stems that we loose detail as in the next
  example

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Percentage of people below the poverty line
for the 50 states and D.C.

• 16.4 10.2 15.9 15.3 17.9 9.0 10.8 8.3 21.2
• 14.9 14.0 8.7 12.0 12.4 13.7 10.7 14.9 18.5
• 25.7 9.4 10.7 9.7 14.1 11.7 19.9 15.6 11.5
• 8.8 11.1 7.7 9.2 21.1 17.0 14.2 10.4 14.1
• 16.7 11.8 12.5 10.3 13.8 14.5 14.6 19.1 8.0
• 7.6 10.7 11.7 18.6 9.0 9.3

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Stem and Leaf Graph for Poverty Data

• 0 88889999999
• 1 00011112222223444444
• 1 55555666778999
• 2 011
• High 25.7
• Prototype 21 21

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Histogram for Poverty Data
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Histograms

• A histogram allows you the flexibility to choose
  your own range of values for the bars
• The range of values for the bars do not have to
  correspond to the stems of the stem-and-leaf plot

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How to Construct a Histogram

• Big idea is to beak the range of data values into
  smaller ranges (bins)
• Construct a bar over each bin
• Height of the bar corresponds to the frequency of
  the data in that bin
• Strive for somewhere between 7 and 15 bins

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Effect of Bin size on Histogram

• The highest point in thousands of feet for each
  of the 50 United States data
• A-5 Uses1 Practice 1

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Interactive Lessons

• A-5 Basics Basics 2 (rounding and creating a
  stem-and-leaf graph)
• A-5 Basics Basics 2 (rounding large numbers and
  creating a stem-and-leaf graph)
• A-5 Basics Practice 3 (creating a stem-and-leaf
  graph together with a histogram)
• A-5 Uses Practice 1 (effect of bins on
  histogram)

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