Describing Data with Graphs

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Chapter 3

• Describing Data with Graphs

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Graphs Such

• What is a graph?
• Pictorial Representation of a frequency
  distribution.

How often
Frequency of Occurrence
this observation occurs.
Observation Type/Class
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A Graph for Qualitative Data

• Bar Graphs fall into the gap!

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Qualitative Data

• Bar Graph
• Used for qualitative data.
• Y-Axis Frequency/Relative Freq
• X-Axis Category
• Height of bar represents the (rel.) frequency of
  occurrence for the category
• Must be a visible gap between the bars
• Represents a discontinuous scale

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Qualitative Data

• Bar Graph Construction
• 1) Create Frequency Distribution
• 2) Make a tick on x-axis for each Observation
  Type/Category
• 3) Label Axis Title Graph appropriately
• 4) For each Category, draw a bar to a height that
  corresponds to the frequency on the Y-axis
• 5) Make sure there is a gap between the bars
• Use Separate Shades/Color

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Qualitative Data
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Qualitative Data
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Quantitative Data

• Histograms

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Quantitative Data

• Histogram
• Used for quantitative data.
• Y-Axis Frequency/Relative Freq
• X-Axis Value Type/Observation Type/Class
• Height of bar represents the (rel.) frequency of
  occurrence for the Value Type/Class
• Must NOT be a gap between bars
• Represents a continuous scale

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Quantitative Data

• Histogram Construction
• 1) Create Frequency Distribution
• 2) Make a tick on x-axis for each Value
  Type/Class
• 3) Label Axis Title Graph appropriately
• 4) For each Value Type/Class, draw a bar to a
  height that corresponds to the frequency on the
  Y-axis
• 5) Make sure there is a NOT gap between the bars
• Use SAME Color/Shading for all bars

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Quantitative Data
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Quantitative Data
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Quantitative Data

• Frequency Polygon

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Quantitative Data

• Frequency Polygons
• Used for quantitative data.
• Y-Axis Frequency/Relative Freq
• X-Axis Value Type/Observation Type/Class
• Height of line represents the (rel.) frequency of
  occurrence for the Value Type/Class
• Ends of polygon must touch the X-axis
• Represents a closed data set

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Quantitative Data

• Frequency Polygon Construction
• 1) Create Frequency Distribution
• 2) Make a tick on x-axis for each Value
  Type/Class
• Add a tick for 1 additional Type/Class below the
  lowest value AND 1 additional Type/Class above
  the lowest value
• 3) Label Axis Title Graph appropriately

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Quantitative Data

• Frequency Polygon Construction
• 4) For each Value Type/Class, draw a dot at
  height that corresponds to the frequency on the
  Y-axis
• 5) Connect the dots
• 6) For the additional low/high classes, place a
  dot on the x-axis and connect to polygon

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Quantitative Data
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Quantitative Data
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Quantitative Data
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Quantitative Data
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Quantitative Data

• Why use frequency polygons?
• Easier to compare different groups!

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Quantitative Data
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Quantitative Data
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Quantitative Data
Weight Class
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Quantitative Data
Weight Class
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Quantitative Data

• Shapes of Distributions

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Distribution Shapes

• 3/4 Types of Shape
• Unimodal
• Normal
• Skew
• Negatively Skewed
• Positively Skewed
• Bimodal

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Shapes

• Unimodal
• One Peak
• One High Score

• Bimodal
• Two Peaks
• Two High Scores
• Two unimodal distributions put together

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Shapes

• Normal
• Unimodal
• Symmetrical
• Bell Shaped

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Shapes

• Positively Skewed
• Unimodal
• Not Symmetrical
• Mostly Low Scores
• Positive Outliers

• Negatively Skewed
• Unimodal
• Not Symmetrical
• Mostly High Scores
• Negative Outliers

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Who Skewed the Data?

• The world would have been normal, but..