L03-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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9/3/09 Lecture 3 1 STOR 155 Introductory Statistics Lecture 3: Displaying Distributions with Numbers The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
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9/3/09 Lecture 3 2 Exploratory Data Analysis (EDA) • Graphical Visualization: Shape – Bar Graph – Pie Chart – Stem plot – Histogram – Time plot ( not for distribution, but for changing pattern over time ) • Numerical Summary: Center and Spread – Center: • Mean, Median and Mode – Spread: • Quartiles, Five-number summary and Boxplot • Standard Deviation
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9/3/09 Lecture 3 3 What is the average highway (city) mileage? What is the ``middle value’’ of highway (city) mileage?
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9/3/09 Lecture 3 4 Measuring center: the mean • Mean = Average value • The sample mean : If the n o bservations in a sample are , then their mean is x i n n x n x x x x 1 2 1 / ) ... ( n x x x ,... , 2 1 x
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9/3/09 Lecture 3 5 Measuring center: the median
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9/3/09 Lecture 3 6 Example: Fuel economy (miles per gallon) for 2004 two-seater cars Look at the Highway mileage (w/o Honda Insight): – Mean – Median How about with Honda Insight? – Mean – Median What can you say?
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9/3/09 Lecture 3 7 Example: Salary Survey of UNC Graduates • Survey a certain number of graduates from UNC. • A lot of departments are surveyed. • Question: – Which department produces students that earn the most on average ten years after they got their degrees? • Answer: – Geography!!!!?????? – Michael Jordan
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9/3/09 Lecture 3 8 Mean vs Median • Mean: – easy to calculate – easy to work with algebraically – highly affected by outliers – Not a resistant measure • Median: – can be time consuming to calculate – more resistant to a few extreme observations (sometimes outliers) – robust
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L03-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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