Displaying Distributions with Graphs

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Chapter 11

• Displaying Distributions with Graphs

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Thought Question 1
Suppose you are comparing two job offers, and one
of your considerations is the cost of living in
each area. You get the local newspapers and
record the price of 50 advertised apartments for
each community. What summary measures of the
rent values for each community would you need in
order to make a useful comparison?
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Thought Question 2
Students in a statistics class at a large state
university were given a survey in which one
question asked was age (in years) one student
was a retired person, and her age was an
outlier. What do you think is meant by an
outlier? If the students heights were
measured, would this same retired person
necessarily have a value that was an outlier?
Explain.
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Turning Quantitative Data Into Information

• Center of the data
• Spread of the data (Variation)
• Shape of the data

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Case Study
Weight Data
STAT 208 Class SurveySpring, 1997 Virginia
Commonwealth University
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Weight Data
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Weight DataStemplot(Stem Leaf)
10 0166 11 009 12 0034578 13 00359 14 08 15
00257 16 555 17 000255 18 000055567 19 245 20
3 21 025 22 0 23 24 25 26 0
Key 203 means203 pounds Stems 10sLeaves
1s
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Weight Data Frequency Table
Left endpoint is included in the group, right
endpoint is not.
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Weight Data Histogram
Weight Left endpoint is included in the group,
right endpoint is not.
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Shape of the Data

• Symmetric
• bell shaped
• other symmetric shapes
• Asymmetric
• right skewed
• left skewed
• Unimodal, bimodal

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Symmetric HistogramsBell-Shaped
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Symmetric HistogramsMound-Shaped
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Symmetric HistogramsUniform
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Asymmetric HistogramsSkewed to the Left
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Asymmetric HistogramsSkewed to the Right
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Outliers

• Extreme values, far from the rest of the data.
• May occur naturally
• May occur due to error in recording
• May occur due to error in measuring
• Observational unit may be fundamentally different

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Number of Books Read for Pleasure
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Key Concepts

• Displays (Stemplots Histograms)
• Graph Shapes
• Symmetric
• Skewed to the Right
• Skewed to the Left
• Outliers