Histograms and Pictures of Data

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Section 2-3 2-4

• Histograms and Pictures of Data

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Why graph?

• Graphics can be used to display a
• data set AND to better understand the nature of
  the distribution of the data.

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Histogram

• A histogram is a bar graph in which the bars
  touch.
• The vertical axis represents frequencies, the
  horizontal axis represents classes.

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Example 1

• How many people attend NFL Super Bowl games?
• Rounded to the nearest thousand, the attendance
  numbers for numerous years (in thousands) are as
  follows
• 62 76 75 81 79 81 90
• 72 81 80 103 76 79 104
• 76 81 104 73 84 74 101
• 73 75 73 74 63 98 72
• Create a histogram of the data.

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Frequency polygon

• A frequency polygon is a line graph which
  connects frequencies located above the
  corresponding midpoints of the classes.
• A polygon is a closed figure, so the line
  segments must begin and end on the x-axis.

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Example 2

• Using the data in example 1, create a frequency
  polygon of the data.

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Stem-and-leaf plot

• A stem-and-leaf plot represents data by
  separating each value into 2 parts
• a stem (left digit(s)) and
• a leaf (right digit(s)).

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Example 3

• Given the following test scores, create a
  stem-and-leaf plot of the data
• 78 65 94 80 83 56 73
• 89 87 78 45 62 100 98
• 60 87 54 92 69 75 84

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• 4 5
• 5 46
• 0259
• 7 3588
• 8 034779
• 248
• 10 0

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Pie chart

• A Pie chart (or circle graph) is generally used
  to show the percentage for each class in terms of
  the whole (100).

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Race/ethnicity of persons (including children)
who received a diagnosis of HIV/AIDS, 2003
Source Centers for Disease Control and
Prevention
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Example 4

• In a national survey conducted by the CDC in
  order to determine health-risk behaviors among
  college students, college students were asked,
  How often do you wear a seat belt when riding in
  a car driven by someone else?

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Scatter Diagram

• A Scatter Diagram is used to graph paired data on
  an x and y-axis.

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Example 5

• The following data is based on information taken
  from the pediatrics section of The Merck Manual.
  
• Let x be the body weight of a child (in kg), and
  let y be the metabolic rate of the child
  (100kcal/24 h)
• x 3.0 5.0 9.0 11.0 15.0 17.0 19.0 21.0
• y 1.4 2.7 5.0 6.0 7.1 7.8 8.3 8.8
• Create a scatter diagram of the data.

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