Chapter 3 Displaying Data Tables and Graphing

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Chapter 3Displaying DataTables and Graphing
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The Value of Charts

• Visual learners will understand concepts and data
  more easily if they are portrayed graphically.
• There are many commonly used graphical techniques
  used in statistics.
• Quantitative people may prefer to look at the
  numeric data. They may prefer to look at data
  tables and spreadsheets.

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Frequency Distributions

• Organized in table form.
• Data Value Frequency

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Frequency Distributions contd

• If there is a lot of data then breaking it into
  Class Intervals may be helpful.
• Intervals must cover the entire range of data
• Intervals should not overlap
• Intervals should all be of the same length

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Example

• Frequency Distribution using Class Intervals
• Class Interval Midpoint Frequency
• 10 14 12 5
• 15- 19 17 12
• 20-24 9 8

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Cumulative Freq Distributions

• Can accumulate Frequencies and also Frequency,
  see Table 3.15, page 46
• Score Freq Freq Cum Freq Cum freq
• 20 3 20 3
  20
• 25 5 33 8
  53
• 30 7 47 15
  100

The Cumulative Frequency Percent is the
Percentile.
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Graphical Display Tools

• Histograms use vertical bars to represent
  frequencies.
• These can be made for discrete data values or for
  class intervals.
• The bars adjoin each other.
• Vertical axis is always frequency
• Horizontal axis represents data values or class
  intervals

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Histograma bar chart for quantitative data
1 2 3 4 5
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Frequency Polygon
1 2 3 4 5
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Histograms and Freq Polygons

• Both can be done cumulatively.
• Both can be done for discrete or class interval
  data
• Both convey the same information. Choice is a
  matter of personal preference.
• A cumulative frequency polygon is also called an
  S-curve or Ogive.

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Ogive

100
80
60
Cumulative Percent Frequency
40
20
Scores
50 60 70 80 90 100
110
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Histograms and Freq Polygons

• Can overlay two Frequency Polygons on the same
  axis for comparison.
• With either x-axis is normally an Interval or
  Ratio scale
• Underlying variable may be discrete or continuous
  but as usual we approximate using discrete
  values.

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Pie Charts

• APA Recommends 4 or 5 wedges. Up to 7 is quite
  common.
• Pie pieces represent non-overlapping categories
• Can label pie pieces with data values and/or
  percent of total.

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Pie Chart
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Bar Graphs

• Can be used for non-quantitative or quantitative
  data. See Histograms.
• Bars normally do not touch by convention
• X-axis scale is usually just a nominal scale
• Can be drawn with bars vertical or horizontal
• Can use joint bars to represent two groups being
  compared

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Bar Graph
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Line Graphs

• Convenient way to compare two or more groups.
• Not a Frequency Polygon
• X-axis is normally a nominal scale

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