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1/22/08
Lecture 4
1
STOR 155 Introductory Statistics
Lecture 4: Displaying
Distributions with Numbers
The
UNIVERSITY
of
NORTH CAROLINA
at
CHAPEL HILL
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Lecture 4
2
Exploratory Data Analysis (EDA)
•
Graphical Visualization:
Shape
–
Bar Graph
–
Pie Chart
–
Stem plot
–
Histogram
–
Time plot (
not for distribution, but for changing pattern across time
)
•
Numerical Summary:
Center
and
Spread
–
Center:
•
Mean and Median
–
Spread:
•
Quartiles, Fivenumber summary and Boxplot
•
Standard Deviation
–
Choose one from each category.
1/22/08
Lecture 4
3
•
What is the average highway (city) mileage?
•
What is the middle value of highway (city) mileage?
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Lecture 4
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
1/22/08
Lecture 4
5
Measuring center: the median
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Lecture 4
6
Example: Fuel economy (miles per gallon) for 2004 twoseater cars
•
Look at the
Highway
mileage (w/o Honda
Insight):
–
Mean
–
Median
•
How about with Honda
Insight?
–
Mean
–
Median
•
What can you say?
1/22/08
Lecture 4
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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Lecture 4
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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This note was uploaded on 03/26/2008 for the course STOR 155 taught by Professor Andrewb.nobel during the Fall '08 term at UNC.
 Fall '08
 AndrewB.Nobel

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