meeting 04 Graphical Presentations
3/5/2011
Tabular and Graphical Procedures
Data
Qualitative Data
Graphical Presentations
Tabular
Methods
Present ed by:
Mahendra AN
Sources:
ht t p: / / business.clayt on.edu/ arj om and/ business/ st at % 20present at ions/ bus
a3101.ht m l
ht t p: / / w w w.cliffsnot es.com / st udy_guide/
Anderson, Sw eeney,w iliam s, St a t ist ics for Busine ss a nd Econom ics ,
10 e, Thom son, 2008
Cardiac Care
Emergency
Intensive Care
Maternity
Surgery
1,052
2,245
340
552
4,630
Tabular
Methods
Graphical
Methods
•Frequency
q
y
Distribution
•Rel. Freq. Dist.
•Cum. Freq. Dist.
•Cum. Rel. Freq.
Distribution
•StemStem-andand-Leaf
Display
•Crosstabulation
(Contingency
Table)
•Bar Graph
•Pie Chart
•Dot Plot
•Histogram
•Ogive
•Scatter
Diagram
Slide 2
Pie Chart Example
Number
of Patients
Hospital
Unit
Cardiac Care
Emergency
Intensive Care
Maternity
Surgery
Hospital Patients by Unit
5000
Number of
patients per year
Hospital
Unit
Graphical
Methods
•Frequency
Distribution
•Rel. Freq. Dist.
•Percent Freq.
Distribution
•Crosstabulation
(Contingency
Table)
Bar Chart Example
Quantitative Data
4000
Number
of Patients
% of
Total
1,052
2,245
340
552
4,630
11.93
25.46
3.86
6.26
52.50
Hospital Patients by Unit
Cardiac Care
12%
3000
Emergency
25%
Surgery
53%
2000
1000
Surgery
Maternity
Intensive
Care
Emergency
Cardiac
Care
0
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Chap 2-3
Intensive Care
4%
Maternity
6%
Chap 2-4
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Stem--andStem
and-Leaf Display
Stem-and-Leaf Diagram
(Percentages
are rounded to
the nearest
percent)
A stem
stem--andand-leaf display shows both the rank order
and shape of the distribution of the data.
It is similar to a histogram on its side, but it has the
advantage of showing the actual data values.
A simple way to see distribution details in a
data set
The first digits of each data item are arranged to the
left of a vertical line.
To the right of the vertical line we record the next
when the leaf unit is
digit for each item in rank order-order--when
not shown, it is assumed to equal 1.
Each line in the display is referred to as a stem
stem..
METHOD: Separate the sorted data series
into leading digits (the stem) and
the trailing digits (the leaves)
Each digit on a stem is a leaf.
leaf.
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Chap 2-5
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
Slide 6
1
3/5/2011
Example
Example
Data in ordered array:
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
(continued)
Here, use the 10’s digit for the stem unit:
Completed stem-and-leaf
stem and leaf diagram:
Stem Leaf
21 is shown as
38 is shown as
Stem
Leaves
2
1
2
3
8
3
0 2 8
4
1
Chap 2-7
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
1 4 4 6 7 7
Chap 2-8
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Stretched StemStem-andand-Leaf Display
Stretched Stem
Stem--andand-Leaf Display
If we believe the original stem
stem--andand-leaf display has
condensed the data too much, we can stretch the
display by using two stems for each leading digit(s).
5
5
6
6
7
7
8
8
9
9
10
10
Whenever a stem value is stated twice, the first value
corresponds to leaf values of 0 − 4, and the second
value corresponds to leaf values of 5 − 9.
9
2
7
2
5
1
5
0
5
1
7
1
5
2
6
1
5
0
8
3
7
4
5
2
7
2
5
2
9
2
8 8 8 9 9 9
2 3 4 4
6 7 8 9 9 9
3
7 8 9
9 The first value
corresponds to
leaf values of
0 - 4, and the
second value
corresponds to
leaf values of
5-9
9
Slide 9
Slide 10
Using other stem units
Leaf Units
•
•
•
•
A single digit is used to define each leaf.
In the preceding example, the leaf unit was 1.
Using the 100’s digit as the stem:
Round off the 10’s digit to form the leaves
Leaf units may be 100
100,, 10
10,, 1, 0.1,
0.1, and so on.
Stem
Where the leaf unit is not shown,
shown it is assumed
to equal 1.
613 would become
6
1
776 would become
7
8
12
2
Slide 11
Leaf
...
1224 becomes
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
Chap 2-12
2
3/5/2011
Example: Leaf Unit = 0.1
Using other stem units
(continued)
If we have data with values such as
8.6
Using the 100’s digit as the stem:
9.4
9.1
10.2
11.0
8.8
a stem
stem--andand-leaf display of these data will be
The completed stem-and-leaf display:
Leaf Unit = 0.1
8 6 8
9 1 4
10 2
11 0 7
Data:
613, 632, 658, 717,
722, 750, 776, 827,
841, 859, 863, 891,
894, 906, 928, 933,
955, 982, 1034, 1047
,1056, 1140, 1169, 1
224
11.7
Stem
6
Leaves
136
7
2258
8
346699
9
13368
10
356
11
47
12
2
Slide 14
Chap 2-13
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Example: Leaf Unit = 10
Histogram
If we have data with values such as
1806 1717 1974 1791 1682 1910 1838
A graph of the data in a frequency distribution
is called a histogram
The interval endpoints are shown on the
horizontal axis
the vertical axis is either frequency, relative
frequency, or percentage
Bars of the appropriate heights are used to
represent the number of observations within
each class
a stem
stem--andand-leaf display of these data will be
Leaf Unit = 10
16 8
17 1 9
18 0 3
19 1 7
The 82 in 1682
is rounded down
to 80 and is
represented as an 8.
You do this for all
of the data.
Slide 15
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Histogram Example
Interval
Pareto Diagram
Frequency
Used to portray categorical data
A bar chart, where categories are shown in
descending
g order of frequency
q
y
A cumulative polygon is often shown in the
same graph
Used to separate the “vital few” from the “trivial
many”
His togram : Daily High Te m pe rature
3
6
5
4
2
7
5
5
4
4
3
3
2
2
1
(No gaps
between
bars)
6
6
Frequency
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
0
Chap 2-16
0
0
0 0 10 10 2020 30 30 40 40 50 50 60 60 70
Temperature in Degrees
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Chap 2-17
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
Chap 2-18
3
3/5/2011
Pareto Diagram Example
Pareto Diagram Example
(continued)
Example: 400 defective items are examined
for cause of defect:
Step 1: Sort by defect cause, in descending order
Step 2: Determine % in each category
Source of
Manufacturing Error
Number of defects
Bad Weld
34
Source of
Manufacturing Error
Number of defects
Poor Alignment
223
Poor Alignment
223
55.75
Missing Part
25
Paint Flaw
78
19.50
8.50
Paint Flaw
78
Bad Weld
34
Electrical Short
19
Missing Part
25
6.25
Cracked case
21
Cracked case
21
5.25
Total
400
Electrical Short
19
4.75
Total
400
100%
Chap 2-19
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Pareto Diagram Example
(continued)
Step 3: Show results graphically
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
{
Pareto Diagram: Cause of Manufacturing Defect
60%
{
100%
90%
80%
70%
40%
60%
50%
30%
40%
20%
30%
20%
10%
10%
0%
cu
umulative % (line graph)
50%
Chap 2-20
Ogive (Cumulative Line Graph)
{
% of defects in each cate
egory
(bar graph)
% of Total Defects
{
{
Dat a m ay be expressed using a single line.
An ogive ( a cum ulat ive line graph) is best used when you
want t o display t he t ot al at any given t im e.
The relat ive slopes from point t o point will indicat e great er
or lesser increases; for exam ple, a st eeper slope m eans a
great er increase t han a m ore gradual slope.
An ogive,
ogive however
however, is not t he ideal graphic for showing
com parisons bet ween cat egories because it sim ply
com bines t he values in each cat egory and t hus indicat es
an accum ulat ion, a growing or lessening t ot al.
I f you sim ply want t o keep t rack of a t ot al and your
individual values are periodically com bined, an ogive is an
appropriat e display.
0%
Poor Alignment
Paint Flaw
Bad Weld
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Ogive example
Missing Part
Cracked case
Electrical Short
Chap 2-21
Dot Plot
{
{
D ot plot s are sim ilar t o bar graphs.
Typically used for a sm all set of
values, a dot plot uses a dot for
each
h unit
it off m easurem entt ;
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
4
3/5/2011
Graphs for Time-Series Data
Dot plot example
I tem
Am ou n t
Tuit ion fees
$5,000
Room and board
9,000
Books and lab
2,000
Clot hes/ cleaning
1,000
Transport at ion
2 000
2,000
I nsurance and
m iscellaneous
1,000
A line chart (time-series plot) is used to show
the values of a variable over time
Time is measured on the horizontal axis
The variable of interest is measured on the
vertical axis
Chap 2-26
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Crosstabulations and Scatter Diagrams
Line Chart Example
As we indicated, often a manager is interested in tabular
and graphical methods that will help understand the
relationship between two variables.
variables.
Magazine Subscriptions by Year
350
Crosstabulation (or Contingency Table)
Table) and a
scatter diagram are two methods for summarizing the
data for two (or more) variables simultaneously.
Thousands of subscribers
s
300
250
200
150
100
50
0
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Crosstabulation Or Contingency Table
Crosstabulation Or Contingency Table
Remember that a crosstabulation is a tabular
summary of data for two variables.
Slide 28
Chap 2-27
Crosstabulation can be used when:
one variable is qualitative and the other is
quantitative,
• both variables are qualitative, or
• both variables are quantitative.
Example: Finger Lakes Homes
The number of Finger Lakes homes sold for each
style and price for the past two years is shown below.
•
Price
Range
As we said, the left and top margin labels define
the classes for the two variables.
quantitative
variable
Home Style
Colonial Log
qualitative
variable
Split AA-Frame Total
< $99,000
> $99,000
18
12
6
14
19
16
12
3
55
Total
30
20
35
15
100
Slide 29
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
45
Slide 30
5
3/5/2011
Crosstabulation Or Contingency Table
Crosstabulation Or Contingency Table
Frequency distribution
for the price variable
Home Style
Colonial Log
Price
Range
Split AA-Frame Total
< $99,000
$99 000
> $99,000
18
12
6
14
19
16
12
3
55
Total
30
20
35
15
100
Insights Gained from Preceding Crosstabulation
•
The greatest number of homes in the sample (19
(19))
are a splitsplit-level style and priced at less than or
$99,000..
equal to $99,000
•
Only three homes in the sample are an AA-Frame
style and priced at more than $99,000.
$99 000
45
Frequency distribution
for the home style variable
Slide 31
Crosstabulation
Row Or Column Percentages?
As we said, converting the entries in the table into
row percentages or column percentages can provide
additional insight about the relationship between
the two variables.
Slide 32
Crosstabulation or Contingency Table
(Row %)
Price
Range
< $99,000
> $99,000
$99 000
Home Style
Colonial Log
32.73
26.67
26 67
Split
10.91 34.55
31
31.11
11 35
35.56
56
AA-Frame Total
21.82
66.67
67
100
100
Note: row totals are actually 100.01 due to rounding.
(Colonial and > $99K)/(All >$99K) x 100 = (12/45) x 100
(Cell Count) (100)
Row Total
Slide 33
Scatter Diagram and Trendline
Crosstabulation or Contingency Table
(Column %)
Price
Range
Home Style
Colonial Log
< $99,000
> $99,000
$99 000
60.00
40.00
40 00
Total
100
Split
30.00 54.29
70
70.00
00 45
45.71
71
100
100
Slide 34
A scatter diagram is a graphical presentation of the
relationship between two quantitative variables.
AA-Frame
One variable is shown on the horizontal axis and the
other variable is shown on the vertical axis.
80.00
20
20.00
00
The general pattern of the plotted points suggests the
overall
ll relationship
l ti
hi b
between
t
th
the variables.
i bl
100
A trendline is a line that provides an approximation
of the relationship.
(Colonial and > $99K)/(All Colonial) x 100 = (12/30) x 100
(Cell Count) (100)
Column Total
Slide 35
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
Slide 36
6
3/5/2011
Scatter Diagram and Trendline
Scatter Diagram and Trendline
A Positive Relationship
y
A Negative Relationship
y
x
x
Slide 37
Slide 38
Scatter Diagram and Trendline
No Apparent Relationship
y
“Te ll m e a n d I for ge t ,
Te a ch m e a n d I r e m e m be r ,
I n volve m e a n d I Le a r n ”
- - Ben Franklin - x
Slide 39
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
7
Tabular and Graphical Procedures
Data
Qualitative Data
Graphical Presentations
Tabular
Methods
Present ed by:
Mahendra AN
Sources:
ht t p: / / business.clayt on.edu/ arj om and/ business/ st at % 20present at ions/ bus
a3101.ht m l
ht t p: / / w w w.cliffsnot es.com / st udy_guide/
Anderson, Sw eeney,w iliam s, St a t ist ics for Busine ss a nd Econom ics ,
10 e, Thom son, 2008
Cardiac Care
Emergency
Intensive Care
Maternity
Surgery
1,052
2,245
340
552
4,630
Tabular
Methods
Graphical
Methods
•Frequency
q
y
Distribution
•Rel. Freq. Dist.
•Cum. Freq. Dist.
•Cum. Rel. Freq.
Distribution
•StemStem-andand-Leaf
Display
•Crosstabulation
(Contingency
Table)
•Bar Graph
•Pie Chart
•Dot Plot
•Histogram
•Ogive
•Scatter
Diagram
Slide 2
Pie Chart Example
Number
of Patients
Hospital
Unit
Cardiac Care
Emergency
Intensive Care
Maternity
Surgery
Hospital Patients by Unit
5000
Number of
patients per year
Hospital
Unit
Graphical
Methods
•Frequency
Distribution
•Rel. Freq. Dist.
•Percent Freq.
Distribution
•Crosstabulation
(Contingency
Table)
Bar Chart Example
Quantitative Data
4000
Number
of Patients
% of
Total
1,052
2,245
340
552
4,630
11.93
25.46
3.86
6.26
52.50
Hospital Patients by Unit
Cardiac Care
12%
3000
Emergency
25%
Surgery
53%
2000
1000
Surgery
Maternity
Intensive
Care
Emergency
Cardiac
Care
0
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Chap 2-3
Intensive Care
4%
Maternity
6%
Chap 2-4
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Stem--andStem
and-Leaf Display
Stem-and-Leaf Diagram
(Percentages
are rounded to
the nearest
percent)
A stem
stem--andand-leaf display shows both the rank order
and shape of the distribution of the data.
It is similar to a histogram on its side, but it has the
advantage of showing the actual data values.
A simple way to see distribution details in a
data set
The first digits of each data item are arranged to the
left of a vertical line.
To the right of the vertical line we record the next
when the leaf unit is
digit for each item in rank order-order--when
not shown, it is assumed to equal 1.
Each line in the display is referred to as a stem
stem..
METHOD: Separate the sorted data series
into leading digits (the stem) and
the trailing digits (the leaves)
Each digit on a stem is a leaf.
leaf.
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Chap 2-5
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
Slide 6
1
3/5/2011
Example
Example
Data in ordered array:
Data in ordered array:
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
21, 24, 24, 26, 27, 27, 30, 32, 38, 41
(continued)
Here, use the 10’s digit for the stem unit:
Completed stem-and-leaf
stem and leaf diagram:
Stem Leaf
21 is shown as
38 is shown as
Stem
Leaves
2
1
2
3
8
3
0 2 8
4
1
Chap 2-7
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
1 4 4 6 7 7
Chap 2-8
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Stretched StemStem-andand-Leaf Display
Stretched Stem
Stem--andand-Leaf Display
If we believe the original stem
stem--andand-leaf display has
condensed the data too much, we can stretch the
display by using two stems for each leading digit(s).
5
5
6
6
7
7
8
8
9
9
10
10
Whenever a stem value is stated twice, the first value
corresponds to leaf values of 0 − 4, and the second
value corresponds to leaf values of 5 − 9.
9
2
7
2
5
1
5
0
5
1
7
1
5
2
6
1
5
0
8
3
7
4
5
2
7
2
5
2
9
2
8 8 8 9 9 9
2 3 4 4
6 7 8 9 9 9
3
7 8 9
9 The first value
corresponds to
leaf values of
0 - 4, and the
second value
corresponds to
leaf values of
5-9
9
Slide 9
Slide 10
Using other stem units
Leaf Units
•
•
•
•
A single digit is used to define each leaf.
In the preceding example, the leaf unit was 1.
Using the 100’s digit as the stem:
Round off the 10’s digit to form the leaves
Leaf units may be 100
100,, 10
10,, 1, 0.1,
0.1, and so on.
Stem
Where the leaf unit is not shown,
shown it is assumed
to equal 1.
613 would become
6
1
776 would become
7
8
12
2
Slide 11
Leaf
...
1224 becomes
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
Chap 2-12
2
3/5/2011
Example: Leaf Unit = 0.1
Using other stem units
(continued)
If we have data with values such as
8.6
Using the 100’s digit as the stem:
9.4
9.1
10.2
11.0
8.8
a stem
stem--andand-leaf display of these data will be
The completed stem-and-leaf display:
Leaf Unit = 0.1
8 6 8
9 1 4
10 2
11 0 7
Data:
613, 632, 658, 717,
722, 750, 776, 827,
841, 859, 863, 891,
894, 906, 928, 933,
955, 982, 1034, 1047
,1056, 1140, 1169, 1
224
11.7
Stem
6
Leaves
136
7
2258
8
346699
9
13368
10
356
11
47
12
2
Slide 14
Chap 2-13
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Example: Leaf Unit = 10
Histogram
If we have data with values such as
1806 1717 1974 1791 1682 1910 1838
A graph of the data in a frequency distribution
is called a histogram
The interval endpoints are shown on the
horizontal axis
the vertical axis is either frequency, relative
frequency, or percentage
Bars of the appropriate heights are used to
represent the number of observations within
each class
a stem
stem--andand-leaf display of these data will be
Leaf Unit = 10
16 8
17 1 9
18 0 3
19 1 7
The 82 in 1682
is rounded down
to 80 and is
represented as an 8.
You do this for all
of the data.
Slide 15
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Histogram Example
Interval
Pareto Diagram
Frequency
Used to portray categorical data
A bar chart, where categories are shown in
descending
g order of frequency
q
y
A cumulative polygon is often shown in the
same graph
Used to separate the “vital few” from the “trivial
many”
His togram : Daily High Te m pe rature
3
6
5
4
2
7
5
5
4
4
3
3
2
2
1
(No gaps
between
bars)
6
6
Frequency
10 but less than 20
20 but less than 30
30 but less than 40
40 but less than 50
50 but less than 60
0
Chap 2-16
0
0
0 0 10 10 2020 30 30 40 40 50 50 60 60 70
Temperature in Degrees
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Chap 2-17
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
Chap 2-18
3
3/5/2011
Pareto Diagram Example
Pareto Diagram Example
(continued)
Example: 400 defective items are examined
for cause of defect:
Step 1: Sort by defect cause, in descending order
Step 2: Determine % in each category
Source of
Manufacturing Error
Number of defects
Bad Weld
34
Source of
Manufacturing Error
Number of defects
Poor Alignment
223
Poor Alignment
223
55.75
Missing Part
25
Paint Flaw
78
19.50
8.50
Paint Flaw
78
Bad Weld
34
Electrical Short
19
Missing Part
25
6.25
Cracked case
21
Cracked case
21
5.25
Total
400
Electrical Short
19
4.75
Total
400
100%
Chap 2-19
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Pareto Diagram Example
(continued)
Step 3: Show results graphically
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
{
Pareto Diagram: Cause of Manufacturing Defect
60%
{
100%
90%
80%
70%
40%
60%
50%
30%
40%
20%
30%
20%
10%
10%
0%
cu
umulative % (line graph)
50%
Chap 2-20
Ogive (Cumulative Line Graph)
{
% of defects in each cate
egory
(bar graph)
% of Total Defects
{
{
Dat a m ay be expressed using a single line.
An ogive ( a cum ulat ive line graph) is best used when you
want t o display t he t ot al at any given t im e.
The relat ive slopes from point t o point will indicat e great er
or lesser increases; for exam ple, a st eeper slope m eans a
great er increase t han a m ore gradual slope.
An ogive,
ogive however
however, is not t he ideal graphic for showing
com parisons bet ween cat egories because it sim ply
com bines t he values in each cat egory and t hus indicat es
an accum ulat ion, a growing or lessening t ot al.
I f you sim ply want t o keep t rack of a t ot al and your
individual values are periodically com bined, an ogive is an
appropriat e display.
0%
Poor Alignment
Paint Flaw
Bad Weld
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Ogive example
Missing Part
Cracked case
Electrical Short
Chap 2-21
Dot Plot
{
{
D ot plot s are sim ilar t o bar graphs.
Typically used for a sm all set of
values, a dot plot uses a dot for
each
h unit
it off m easurem entt ;
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
4
3/5/2011
Graphs for Time-Series Data
Dot plot example
I tem
Am ou n t
Tuit ion fees
$5,000
Room and board
9,000
Books and lab
2,000
Clot hes/ cleaning
1,000
Transport at ion
2 000
2,000
I nsurance and
m iscellaneous
1,000
A line chart (time-series plot) is used to show
the values of a variable over time
Time is measured on the horizontal axis
The variable of interest is measured on the
vertical axis
Chap 2-26
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Crosstabulations and Scatter Diagrams
Line Chart Example
As we indicated, often a manager is interested in tabular
and graphical methods that will help understand the
relationship between two variables.
variables.
Magazine Subscriptions by Year
350
Crosstabulation (or Contingency Table)
Table) and a
scatter diagram are two methods for summarizing the
data for two (or more) variables simultaneously.
Thousands of subscribers
s
300
250
200
150
100
50
0
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
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1991
1990
Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc.
Crosstabulation Or Contingency Table
Crosstabulation Or Contingency Table
Remember that a crosstabulation is a tabular
summary of data for two variables.
Slide 28
Chap 2-27
Crosstabulation can be used when:
one variable is qualitative and the other is
quantitative,
• both variables are qualitative, or
• both variables are quantitative.
Example: Finger Lakes Homes
The number of Finger Lakes homes sold for each
style and price for the past two years is shown below.
•
Price
Range
As we said, the left and top margin labels define
the classes for the two variables.
quantitative
variable
Home Style
Colonial Log
qualitative
variable
Split AA-Frame Total
< $99,000
> $99,000
18
12
6
14
19
16
12
3
55
Total
30
20
35
15
100
Slide 29
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
45
Slide 30
5
3/5/2011
Crosstabulation Or Contingency Table
Crosstabulation Or Contingency Table
Frequency distribution
for the price variable
Home Style
Colonial Log
Price
Range
Split AA-Frame Total
< $99,000
$99 000
> $99,000
18
12
6
14
19
16
12
3
55
Total
30
20
35
15
100
Insights Gained from Preceding Crosstabulation
•
The greatest number of homes in the sample (19
(19))
are a splitsplit-level style and priced at less than or
$99,000..
equal to $99,000
•
Only three homes in the sample are an AA-Frame
style and priced at more than $99,000.
$99 000
45
Frequency distribution
for the home style variable
Slide 31
Crosstabulation
Row Or Column Percentages?
As we said, converting the entries in the table into
row percentages or column percentages can provide
additional insight about the relationship between
the two variables.
Slide 32
Crosstabulation or Contingency Table
(Row %)
Price
Range
< $99,000
> $99,000
$99 000
Home Style
Colonial Log
32.73
26.67
26 67
Split
10.91 34.55
31
31.11
11 35
35.56
56
AA-Frame Total
21.82
66.67
67
100
100
Note: row totals are actually 100.01 due to rounding.
(Colonial and > $99K)/(All >$99K) x 100 = (12/45) x 100
(Cell Count) (100)
Row Total
Slide 33
Scatter Diagram and Trendline
Crosstabulation or Contingency Table
(Column %)
Price
Range
Home Style
Colonial Log
< $99,000
> $99,000
$99 000
60.00
40.00
40 00
Total
100
Split
30.00 54.29
70
70.00
00 45
45.71
71
100
100
Slide 34
A scatter diagram is a graphical presentation of the
relationship between two quantitative variables.
AA-Frame
One variable is shown on the horizontal axis and the
other variable is shown on the vertical axis.
80.00
20
20.00
00
The general pattern of the plotted points suggests the
overall
ll relationship
l ti
hi b
between
t
th
the variables.
i bl
100
A trendline is a line that provides an approximation
of the relationship.
(Colonial and > $99K)/(All Colonial) x 100 = (12/30) x 100
(Cell Count) (100)
Column Total
Slide 35
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
Slide 36
6
3/5/2011
Scatter Diagram and Trendline
Scatter Diagram and Trendline
A Positive Relationship
y
A Negative Relationship
y
x
x
Slide 37
Slide 38
Scatter Diagram and Trendline
No Apparent Relationship
y
“Te ll m e a n d I for ge t ,
Te a ch m e a n d I r e m e m be r ,
I n volve m e a n d I Le a r n ”
- - Ben Franklin - x
Slide 39
© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!
7