Section 2.2
More Graphs and
Displays
Statistics
Mrs. Spitz
Fall 2008
Objectives:
§ How to graph quantitative data sets using
stem-and-leaf plots and dot plots
§ How to graph qualitative data using pie
charts and Pareto charts
§ How to graph paired data sets using
scatter plots and time series charts.
Assignment: pp. 51-54 #1-30
Larson/Farber Ch 2
Graphing Quantitative Data Sets – don’t write
this down.
§ In Section 2.1, you learned several
traditional ways to display quantitative
data graphically. In this section, you will
learn a newer way to display quantitative
data called a stem-and-leaf plot. Stemand-leaf plots are examples of exploratory
data analysis (EDA), which was developed
by John Tukey in 1977.
Larson/Farber Ch 2
Graphing Quantitative Data Sets – don’t write
this down.
§ In a stem and leaf plot, each number is
separated into a stem (the entry’s leftmost
digits) and a leaf (the rightmost digit). A
stem-and-leaf plot is similar to a histogram
but has the advantage that the graph still
contains the original data values. Another
advantage is that it provides an easy way
to sort data.
Larson/Farber Ch 2
Stem-and-Leaf Plot
Lowest value is 67 and highest value is 125, so list
stems from 6 to 12.
102
Stem
6|
7|
8|
9|
10 |
11 |
12 |
Larson/Farber Ch 2
124
Leaf
6
2
4
108
86
103
82
To see complete
display, go to next
slide.
2
8
3
Divide each data value into a stem and a
leaf. The leaf is the rightmost significant digit.
The stem consists of the digits to the left.
The data shown represent the first line of the
‘minutes on phone’ data used earlier. The
complete stem and leaf will be shown on the
next slide.
Stem-and-Leaf Plot
Key: 6 | 7 means 67
6 |7
7 |18
It is very important to use a
8 |25677
key to explain the plot. 6|7
could mean 6700 or .067 for
9 |25799
a different problem. A stem
leaf should not be used
10 | 0 1 2 3 3 4 5 5 7 8 9 and
with data when values are
very different such as 3,
11 | 2 6 8
34,900, 24 etc. The stem-and
leaf has the advantage over a
12 | 2 4 5
histogram of retaining the
original values.
Larson/Farber Ch 2
Stem-and-Leaf with two lines per stem
Key: 6 | 7 means 67
1st line digits 0 1 2 3 4
2nd line digits 5 6 7 8 9
1st line digits 0 1 2 3 4
2nd line digits 5 6 7 8 9
With two lines per stem the data is more finely “chopped”. Class width is
5 times the leaf unit. All stems except possibly the first and last must have
two lines even if one is blank. For this data set, the first line for the stem 6
can be blank because there are no data values from 60 to 64.
Larson/Farber Ch 2
6|7
7|1
7|8
8|2
8|5677
9|2
9|5799
10 | 0 1 2 3 3 4
10 | 5 5 7 8 9
11 | 2
11 | 6 8
12 | 2 4
12 | 5
Dot Plots
§ You can also use a dot plot to graph
quantitative data. In a dot plot, each data
entry is plotted, using a point, above a
horizontal axis. Like a stem-and-leaf plot,
a dot plot allows you to see how data are
distributed and determine specific data
entries.
Larson/Farber Ch 2
Dot Plot
Phone
66
76
86
96
106
minutes
Dot plots also allow you to retain original
values.
Larson/Farber Ch 2
116
126
Graphing Qualitative Data Sets
§ Pie charts provide a convenient way to
present qualitative data graphically. A pie
chart is a circle graph that shows
relationships of parts to a whole.
Larson/Farber Ch 2
Pie Chart
• Used to describe parts of a whole
• Central Angle for each segment
Pie charts help
visualize the relative
proportion of each
category. Find the
relative frequency
for each category
and multiply it by
360 degrees to find
the central angle.
Larson/Farber Ch 2
NASA budget (billions of $) divided
among 3 categories.
Billions of $
Human Space Flight
5.7
Technology
5.9
Mission Support
2.7
Construct a pie chart for the data.
Pie Chart
Billions of $
Human Space Flight
Technology
Mission Support
Total
5.7
5.9
2.7
14.3
Degrees
143
149
68
360
Mission
Support
19%
Human
Space Flight
40%
Technology
41%
Larson/Farber Ch 2
NASA Budget
(Billions of $)
You will need a protractor and a compass.
1.
2.
3.
4.
5.
Take the part and divide it by the whole, and you will
get a decimal. Multiply by 360 and you will get the
number of degrees in that part of the circle. Do this
until you have 360 degrees.
Draw a circle. Starting from the middle of the circle,
draw a line from the center of the circle to the side of
the circle. This is your starting point for 0 degrees.
Use your protractor to measure the number of degrees
required, mark and draw another line from the center
to the edge.
Start at the edge of the next to begin measuring your
next cut in the pie. Continue until you are done.
Yes, you have to do a few by hand so you get the idea.
Later, we will use Excel to create pie charts.
Larson/Farber Ch 2
Pareto Chart
§ Another way to graph qualitative data is to
use a Pareto chart. A Pareto chart is a
vertical bar graph in which the height of
each bar represents frequency or relative
frequency. The bars are positioned in
order of decreasing height with the tallest
bar positioned at the left. Such positioning
helps highlight important data and is used
frequently in business.
Larson/Farber Ch 2
Example Pareto Chart
§ Last year, the retail industry lost $40.9 million in
inventory shrinkage. The causes of the
inventory shrinkage are administrative error
($7.8 million), employee theft ($15.6 million),
shoplifting ($14.7 million), and vendor fraud
($2.9 million). If you were a retailer, which
causes of inventory shrinkage would you
address first? Construct a Pareto chart to show
which causes would be addressed first.
Larson/Farber Ch 2
You can use Excel to make a Pareto Chart
Causes of Inventory Shrinkage
18.0
16.0
14.0
Millions of Dollars
12.0
10.0
8.0
6.0
4.0
2.0
0.0
Employee theft
Shoplifting
Admin Error
Cause
Larson/Farber Ch 2
Vendor Fraud
Graphing Paired Data Sets
§ If two data sets have the same number of entries, and
each entry in the first data set corresponds to one entry
in the second data set, the sets are called paired data
sets. For instance, suppose, a data set contains the
costs of an item and a second data set contains the
sales amounts for the item at each cost. Because each
cost corresponds to a sales amount, the data sets are
paired. One way to graph paired data sets is to use a
scatter plot, where the ordered pairs are graphed as
points in a coordinate plane.
Larson/Farber Ch 2
Scatter Plot
Final
grade
(y)
Absences
x
8
2
5
12
15
9
6
95
90
85
80
75
70
65
60
55
50
45
40
0
2
4
6
8
10
12
Absences (x)
Larson/Farber Ch 2
14
16
Grade
y
78
92
90
58
43
74
81
Time Series
§ A data set that is composed of entries
taken at regular intervals over a period of
time is a time series. For instance, the
amount of precipitation measured each
day for one month is an example of a time
series. You can use a time series chart to
graph a time series.
Larson/Farber Ch 2
Constructing a Time Series Chart
§ The table lists a number
of cellular telephone
subscribers in millions,
and a subscriber’s
average local monthly bill
for service, in dollars, for
the years 1987 through
1996. Construct a time
series chart for the
number of cellular
subscribers. What can
you conclude?
Larson/Farber Ch 2
Year
Subscribers
Average bill
1987
1.2
96.83
1988
2.1
98.02
1989
3.5
89.30
1990
5.3
80.90
1991
7.6
72.74
1992
11.0
68.68
1993
16.0
61.48
1994
24.1
56.21
1995
33.8
51.00
1996
44.0
47.70
Constructing a Time Series Chart
§ Let the horizontal axis represent the years and the vertical axis
represent the number of subscribers in millions. Then plot the paired
data. From the graph, you can see the number of subscribers has
been increasing since 1987. Recent years show greater increases.
Cellular Phone Subscribers (1987-1996)
50
45
40
Subscirbers (in Millions)
35
30
25
20
15
10
5
0
1986
1987
Larson/Farber Ch 2
1988
1989
1990
1991
1992
Year
1993
1994
1995
1996
1997