L4-ss - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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5/13/11 Lecture 4 1 STOR 155 Introductory Statistics Lecture 4: Displaying Distributions with Numbers (II) The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
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5/13/11 Lecture 4 2 Numerical Summary for Distributions • Center – Mean – Median – Mode • Spread – Quartiles, IQR, Five-number summary and Boxplot – Standard Deviation (starting from page14 )
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5/13/11 Lecture 4 3 Examples: 2004 Two-Seater Cars • Highway mileages of the 21 two-seater cars: 13 15 16 16 17 19 20 22 23 23 23 24 25 25 26 28 28 28 29 32 66 • Q1 =18 • Q3 =28 • IQR = Q3 – Q1=10 • 1.5*IQR=15 • Q3+1.5*IQR=43 • Q1-1.5*IQR=3 • 66 is a suspected outlier.
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5/13/11 Lecture 4 4 The five-number summary • To get a quick summary of both center and spread, use the following five-number summary: Minimum Q1 M Q3 Maximum
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5/13/11 Lecture 4 5 Example: HWY Gas Mileage of 2004 Two-seater/Mini Cars • Two-seater – Five-number summary: • 13, 18, 23, 27, 32 • Mini-compact – Five-number summary: • 19, 23, 26, 29, 32
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5/13/11 Lecture 4 6 Boxplots • a visual representation of the five-number summary. • A boxplot consists of – A central box spans the quartiles Q1 and Q3. – A line inside the box marks the median M. – Lines extend from the box out to the smallest and largest observations.
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5/13/11 Lecture 4 7 Boxplots of highway/city gas mileages (Two-seaters/minicompacts)
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5/13/11 Lecture 4 8 Pros and cons of Boxplots • Location of the median line in the box indicates symmetry/asymmetry. • Best used for side-by-side comparison of more than one distribution at a glance. • Less detailed than histograms or stem plots. • The box focuses attention on the central half of the data.
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Lecture 4 9 Income for different Education Level
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L4-ss - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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