Transcript Slide 1

Practice – Ch4

#26: A meteorologist preparing a talk about global
warming compiled a list of weekly low temperatures (in
degrees Fahrenheit) he observed at his south Florida
home last year. The coldest temp. for any week was 36F,
but he inadvertently recorded the Celsius value of 2
degrees. Assuming he correctly listed all the other
temperatures, explain how this error will affect these
summary statistics:
 Measures of center: mean and median
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Mean will be smaller, Median will not be affected
Measures of spread: range, IQR, and standard
deviation
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The range and standard deviation will be larger, the IQR won’t
change.
Copyright © 2009 Pearson Education, Inc.
Slide 4- 1
StatCrunch lab – ch 4

Open StatCrunch from the CourseCompass website
 Select Emails from the Chapter 4 data sets

A university teacher saved every email received from students in a
large Introductory Statistics class during an entire term. She then
counted, for each student who had sent her at least email, how
many e-mails each student had sent.
 Create a histogram of the data – be sure to set bin-width at 1
and to start bins at 1 (why?)
 What are the appropriate labels for the X and Y axes?
(remember, think first, then show, then tell)
 Given the histogram, would you expect the mean or median be
larger? Why?
 Calculate summary statistics (Stat -> Summary Stats ->
Columns) including the 5 number summary and mean and s.d.
 Describe the distribution in terms of shape (modes,
symmetric/skewed, unusual features), center (median or
mean), and spread (IQR or s.d.). Use complete sentences!
Copyright © 2009 Pearson Education, Inc.
Slide 1- 2
Chapter 5
Understanding and
Comparing Distributions
Copyright © 2009 Pearson Education, Inc.
Objectives

The student will be able to:
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Construct a boxplot by hand from a five-number
summary.
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Describe the distribution of a quantitative variable
with a description of the shape of the distribution, a
numerical measure of center, and a numerical
measure of spread.
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Compare the distributions of two or more groups by
comparing their shapes, centers, and spreads.
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Compare two or more groups by comparing their
boxplots.

Use the 1.5 IQR rule to identify possible outliers.
Copyright © 2009 Pearson Education, Inc.
Slide 3- 4
The Five-Number Summary

Recall: the five-number
summary of a distribution
reports its median,
quartiles, and extremes
(maximum and minimum).
 Example: The fivenumber summary for
the daily wind speed is:
Copyright © 2009 Pearson Education, Inc.
Max
8.67
Q3
2.93
Median
1.90
Q1
1.15
Min
0.20
Slide 1- 5
Daily Wind Speed: Making Boxplots
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A boxplot is a graphical display of the fivenumber summary.
Boxplots are particularly useful when comparing
groups.
Two kinds of boxplots – simple and modified.
 In a simple boxplot you only need to know the
5 number summary – whiskers will extend to
the max and min.
 A modified boxplot extends whiskers to the
max and min values within 1.5*IQR of the
quartiles. Outliers are marked separately. Slide 1- 6
Copyright © 2009 Pearson Education, Inc.
Practice

Construct a simple and modified boxplot of our
class data on # of siblings –
 Use your calculator to find the five number
summary
 Then Draw the Boxplots by hand
Copyright © 2009 Pearson Education, Inc.
Slide 1- 7
Constructing Boxplots
1.
Draw a single vertical
axis spanning the range
of the data. Draw short
horizontal lines at the
lower and upper
quartiles and at the
median. Then connect
them with vertical lines
to form a box.
Copyright © 2009 Pearson Education, Inc.
Slide 1- 8
Constructing Boxplots (cont.)
2.
Erect “fences” around the
main part of the data.

The upper fence is 1.5
IQRs above the upper
quartile.

The lower fence is 1.5
IQRs below the lower
quartile.

Note: the fences only help
with constructing the
boxplot and should not
appear in the final display.
Copyright © 2009 Pearson Education, Inc.
Slide 1- 9
Constructing Boxplots (cont.)
3.
Use the fences to grow
“whiskers.”
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Draw lines from the
ends of the box up
and down to the most
extreme data values
found within the
fences.

If a data value falls
outside one of the
fences, we do not
connect it with a
whisker.
Copyright © 2009 Pearson Education, Inc.
Slide 1- 10
Constructing Boxplots (cont.)
4. Add the outliers by
displaying any data
values beyond the
fences with special
symbols.

We often use a
different symbol for
“far outliers” that are
farther than 3 IQRs
from the quartiles.
Copyright © 2009 Pearson Education, Inc.
Slide 1- 11
Wind Speed: Making Boxplots (cont.)

Compare the histogram and boxplot for daily wind speeds:

How does each display represent the distribution?
Copyright © 2009 Pearson Education, Inc.
Slide 1- 12
Comparing Groups

It is always more interesting to compare groups.
With histograms, note the shapes, centers, and spreads
of the two distributions.

What does this graphical display tell you?

Copyright © 2009 Pearson Education, Inc.
Slide 1- 13
Comparing Groups (cont)
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Boxplots offer an ideal balance of information and simplicity,
hiding the details while displaying the overall summary
information.
We often plot them side by side for groups or categories we wish
to compare.
What do these boxplots tell you?
Copyright © 2009 Pearson Education, Inc.
Slide 1- 14
What About Outliers?
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If there are any clear outliers and you are
reporting the mean and standard deviation, report
them with the outliers present and with the
outliers removed. The differences may be quite
revealing.
Note: The median and IQR are not likely to be
affected by the outliers.
Copyright © 2009 Pearson Education, Inc.
Slide 1- 15
Examples

Returning to our class data set – lets use our 5 number summary
of number of siblings to construct a boxplot.
Here are the weekly payrolls for two
imaginary restaurants:
 Draw parallel boxplots (by hand)
 Write a few sentences comparing the
distributions
 Where would you rather work and why?

Moose- McTofu
burgers
123
110
136
115
144
130
150
100
110
120
131
146
140
117
160
129
120
360
130
132
107
Copyright © 2009 Pearson Education, Inc.
Slide 1- 16
Using the TI to make and compare boxplots
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Similar to plotting histograms
Enter data in lists,
To turn on stat plots, STATPLOT-> Plot1 ->
ENTER
 Select On -> Enter
 select the first boxplot pictured (this is a
modified boxplot and indicates outliers
rather than a standard boxplot whose
whiskers extend to the max and minimum),
 Xlist (L1 or L2)
 Frequency (will be 1 if all data is entered,
may be another list if using a frequency
table)
Use Plot2 to display another data set
Zoom -> 9 (ZoomStat)
Use trace to explore the box plot
Copyright © 2009 Pearson Education, Inc.
Moose- McTofu
burgers
123
110
136
115
144
130
150
100
110
120
131
146
140
117
160
129
120
360
130
132
107
Slide 1- 17
Using StatCrunch to make boxplots
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
Enter StatCrunch from the textbook site

Load data: Wines
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Graphs -> Boxplot
 Select Columns: CasePrice
 Group by: Location
 “Plot groups for each column” will create one graph with multiple
boxplots
 “Plot columns for each group” will create multiple separate
boxplots
 Click Next
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Check “Use fences to identify outliers”
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Fill in Y axis label
Use the “Plot groups for each column” boxplot to answer these questions
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Which lake region produces the most expensive wine?
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Which lake region produces the lease expensive wine?
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In which region are the wines generally more expensive?
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Write a few sentences describing these wine prices?
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Slide 1- 18
Practice
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Text #10, #25
Copyright © 2009 Pearson Education, Inc.
Slide 1- 19