Anderson
u
Sweeney
u
Williams
CONTEMPORARY
BUSINESS
STATISTICS
WITH MICROSOFT EXCEL
u Slides Prepared by JOHN LOUCKS u
© 2001 South-Western/Thomson Learning
Slide 1
Chapter 2
Descriptive Statistics I:
Tabular and Graphical Methods




Summarizing Qualitative
Data
Summarizing Quantitative
Data
Exploratory Data Analysis
Crosstabulations
and Scatter Diagrams
Slide 2
Summarizing Qualitative Data





Frequency Distribution
Relative Frequency
Percent Frequency Distribution
Bar Graph
Pie Chart
Slide 3
Frequency Distribution


A frequency distribution is a tabular summary of
data showing the frequency (or number) of items in
each of several nonoverlapping classes.
The objective is to provide insights about the data
that cannot be quickly obtained by looking only at
the original data.
Slide 4
Example: Marada Inn
Guests staying at Marada Inn were asked to rate the
quality of their accommodations as being excellent,
above average, average, below average, or poor. The
ratings provided by a sample of 20 quests are shown
below.
Below Average Average
Above Average
Above Average Above Average Above Average
Above Average Below Average
Below Average
Average
Poor
Poor
Above Average Excellent
Above Average
Average
Above Average
Average
Above Average Average
Slide 5
Example: Marada Inn

Frequency Distribution
Rating
Frequency
Poor
2
Below Average
3
Average
5
Above Average
9
Excellent
1
Total
20
Slide 6
Using Excel’s COUNTIF Function
to Construct a Frequency Distribution

1
2
3
4
5
6
7
8
Formula Worksheet
A
Quality Rating
Above Average
Below Average
Above Average
Average
Average
Above Average
Above Average
B
C
Quality Rating
Poor
Below Average
Average
Above Average
Excellent
Total
D
Frequency
=COUNTIF($A$2:$A$21,C2)
=COUNTIF($A$2:$A$21,C3)
=COUNTIF($A$2:$A$21,C4)
=COUNTIF($A$2:$A$21,C5)
=COUNTIF($A$2:$A$21,C6)
=SUM(D2:D6)
Note: Rows 9-21 are not shown.
Slide 7
Using Excel’s COUNTIF Function
to Construct a Frequency Distribution

1
2
3
4
5
6
7
8
Value Worksheet
A
Quality Rating
Above Average
Below Average
Above Average
Average
Average
Above Average
Above Average
B
C
Quality Rating
Poor
Below Average
Average
Above Average
Excellent
Total
D
Frequency
2
3
5
9
1
20
Note: Rows 9-21 are not shown.
Slide 8
Relative Frequency and
Percent Frequency Distributions




The relative frequency of a class is the fraction or
proportion of the total number of data items
belonging to the class.
A relative frequency distribution is a tabular
summary of a set of data showing the relative
frequency for each class.
The percent frequency of a class is the relative
frequency multiplied by 100.
A percent frequency distribution is a tabular
summary of a set of data showing the percent
frequency for each class.
Slide 9
Example: Marada Inn

Relative Frequency and Percent Frequency
Distributions
Relative
Percent
Rating
Frequency Frequency
Poor
.10
10
Below Average
.15
15
Average
.25
25
Above Average
.45
45
Excellent
.05
5
Total
1.00
100
Slide 10
Using Excel to Construct Relative Frequency
and Percent Frequency Distributions

1
2
3
4
5
6
7
8
Formula Worksheet
C
D
Quality Rating
Poor
Below Average
Average
Above Average
Excellent
Total
Frequency
=COUNTIF($A$2:$A$21,C2)
=COUNTIF($A$2:$A$21,C3)
=COUNTIF($A$2:$A$21,C4)
=COUNTIF($A$2:$A$21,C5)
=COUNTIF($A$2:$A$21,C6)
=SUM(D2:D6)
E
Relative
Frequency
=D2/$D$7
=D3/$D$7
=D4/$D$7
=D5/$D$7
=D6/$D$7
=SUM(E2:E6)
F
Percent
Frequency
=E2*100
=E3*100
=E4*100
=E5*100
=E6*100
=SUM(F2:F6)
Note: Rows 9-21 and Columns A-B are not shown.
Slide 11
Using Excel to Construct Relative Frequency
and Percent Frequency Distributions

Value Worksheet
C
1
2
3
4
5
6
7
8
Quality Rating
Poor
Below Average
Average
Above Average
Excellent
Total
D
Frequency
2
3
5
9
1
20
E
Relative
Frequency
0.10
0.15
0.25
0.45
0.05
1.00
F
Percent
Frequency
10
15
25
45
5
100
Note: Rows 9-21 and Columns A-B are not shown.
Slide 12
Bar Graph





A bar graph is a graphical device for depicting
qualitative data that have been summarized in a
frequency, relative frequency, or percent frequency
distribution.
On the horizontal axis we specify the labels that are
used for each of the classes.
A frequency, relative frequency, or percent frequency
scale can be used for the vertical axis.
Using a bar of fixed width drawn above each class
label, we extend the height appropriately.
The bars are separated to emphasize the fact that
each class is a separate category.
Slide 13
Example: Marada Inn

Bar Graph
9
8
Frequency
7
6
5
4
3
2
1
Poor
Below Average Above Excellent
Average
Average
Rating
Slide 14
Using Excel’s Chart Wizard
to Construct Bar Graphs
Step 1 Select cells A1:A21
Step 2 Select the Chart Wizard button
Step 3 When the Chart Type dialog box appears:
Choose Column in the Chart type list
Choose Clustered Column from the Chart
sub-type display
Select Next >
Step 4 When the Chart Source Data dialog box appears
Select Next >
… continued
Slide 15
Using Excel’s Chart Wizard
to Construct Bar Graphs
Step 5 When the Chart Options dialog box appears:
Select the Titles tab and then
Type Bar Graph of Quality Ratings in the
Chart title box
Enter Quality Rating in the Value (X) axis box
Enter Frequency in the Value (Y) axis box
Select the Legend tab and then
Remove the check in the Show Legend box
Select Next >
… continued
Slide 16
Using Excel’s Chart Wizard
to Construct Bar Graphs
Step 6 When the Chart Location dialog box appears:
Specify the location for the new chart
Select Finish to display the bar graph
Slide 17
Using Excel’s Chart Wizard
to Construct Bar Graphs
Bar Graph of Quality Ratings
Frequency
9
10
11
12
13
14
15
16
17
18
19
20
21
E
D
C
10
8
6
4
2
0
Poor
Below
Average
Average
Above
Average
Excellent
Quality Rating
Slide 18
Pie Chart



The pie chart is a commonly used graphical device
for presenting relative frequency distributions for
qualitative data.
First draw a circle; then use the relative frequencies
to subdivide the circle into sectors that correspond to
the relative frequency for each class.
Since there are 360 degrees in a circle, a class with a
relative frequency of .25 would consume .25(360) =
90 degrees of the circle.
Slide 19
Example: Marada Inn

Pie Chart
Exc.
Poor
5%
10%
Above
Average
45%
Below
Average
15%
Average
25%
Quality Ratings
Slide 20
Summarizing Quantitative Data




Frequency Distribution
Relative Frequency and Percent Frequency
Distributions
Histogram
Cumulative Distributions
Slide 21
Example: Hudson Auto Repair
The manager of Hudson Auto would like to get a
better picture of the distribution of costs for engine
tune-up parts. A sample of 50 customer invoices has
been taken and the costs of parts, rounded to the
nearest dollar, are listed below.
91
71
104
85
62
78
69
74
97
82
93
72
62
88
98
57
89
68
68
101
75
66
97
83
79
52
75
105
68
105
99
79
77
71
79
80
75
65
69
69
97
72
80
67
62
62
76
109
74
73
Slide 22
Frequency Distribution


Guidelines for Selecting Number of Classes
• Use between 5 and 20 classes.
• Data sets with a larger number of elements
usually require a larger number of classes.
• Smaller data sets usually require fewer classes.
Guidelines for Selecting Width of Classes
• Use classes of equal width.
• Approximate Class Width =
Largest Data Value  Smallest Data Value
Number of Classes
Slide 23
Example: Hudson Auto Repair

Frequency Distribution
If we choose six classes:
Approximate Class Width = (109 - 52)/6 = 9.5 10
Cost ($)
50-59
60-69
70-79
80-89
90-99
100-109
Frequency
2
13
16
7
7
5
Total
50
Slide 24
Using Excel’s FREQUENCY Function
to Construct a Frequency Distribution

Formula Worksheet (showing data entered)
1
2
3
4
5
6
7
8
A
B
Parts
Cost
91
71
104
85
62
78
69
C
Parts
Cost
50-59
60-69
70-79
80-89
90-99
100-109
D
Frequency
Slide 25
Using Excel’s FREQUENCY Function
to Construct a Frequency Distribution




The FREQUENCY function is not a “simple” Excel
function.
FREQUENCY is capable of providing multiple
values.
In Excel, a formula that can return multiple values is
called an array formula.
An array formula must be entered in a special way.
Slide 26
Using Excel’s FREQUENCY Function
to Construct a Frequency Distribution

Entering the Necessary Array Formula
Step 1 Select D2:D7 (where the frequencies will appear)
Step 2 Type the following formula:
=FREQUENCY(A2:A51,{59,69,79,89,99,109})
Step 3 Hold down CTRL and SHIFT keys while
pressing ENTER key
(Array formula will be entered in D2:D7)
Slide 27
Using Excel’s FREQUENCY Function
to Construct a Frequency Distribution

Value Worksheet
1
2
3
4
5
6
7
8
A
B
Parts
Cost
91
71
104
85
62
78
69
C
Parts
Cost
50-59
60-69
70-79
80-89
90-99
100-109
D
Frequency
2
13
16
7
7
5
Slide 28
Example: Hudson Auto Repair

Relative Frequency and Percent Frequency
Distributions
Relative
Percent
Cost ($) Frequency
Frequency
50-59
.04
4
60-69
.26
26
70-79
.32
32
80-89
.14
14
90-99
.14
14
100-109
.10
10
Total 1.00
100
Slide 29
Histogram




Another common graphical presentation of
quantitative data is a histogram.
The variable of interest is placed on the horizontal
axis and the frequency, relative frequency, or percent
frequency is placed on the vertical axis.
A rectangle is drawn above each class interval with
its height corresponding to the interval’s frequency,
relative frequency, or percent frequency.
Unlike a bar graph, a histogram has no natural
separation between rectangles of adjacent classes.
Slide 30
Example: Hudson Auto Repair
Histogram
18
16
14
Frequency

12
10
8
6
4
2
50
60
70
80
90
100
110
Cost ($)
Slide 31
Using Excel’s Chart Wizard
to Construct a Histogram
Step 1 Select cells C1:D7
Step 2 Select the Chart Wizard button
Step 3 When the Chart Type dialog box appears:
Choose Column in the Chart type list
Choose Clustered Column from the Chart
sub-type display
Select Next >
Step 4 When the Chart Source Data dialog box appears
Select Next >
… continued
Slide 32
Using Excel’s Chart Wizard
to Construct a Histogram
Step 5 When the Chart Options dialog box appears:
Select the Titles tab and then
Type Histogram for Parts Cost Data in the
Chart title box
Enter Parts Cost ($) in the Value (X) axis box
Enter Frequency in the Value (Y) axis box
Select the Legend tab and then
Remove the check in the Show Legend box
Select Next >
… continued
Slide 33
Using Excel’s Chart Wizard
to Construct a Histogram
Step 6 When the Chart Location dialog box appears:
Specify the location for the new chart
Select Finish to display the histogram
Slide 34
Using Excel’s Chart Wizard
to Construct a Histogram
C
E
Histogram for Parts Cost Data
20
Frequency
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
D
15
10
5
0
50-59
60-69
70-79
80-89
90-99
100-109
Parts Cost ($)
Slide 35
Using Excel’s Chart Wizard
to Construct a Histogram

Eliminating Gaps Between Rectangles
Step 1 Right click on any rectangle in the column chart
Step 2 Select the Format Data Series option
Step 3 When the Format Data Series Option dialog box
appears:
Select the Options tab and then
Enter 0 in the Gap width box
Select OK
Slide 36
Using Excel’s Chart Wizard
to Construct a Histogram
C
E
Histogram for Parts Cost Data
20
Frequency
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
D
15
10
5
0
50-59
60-69
70-79
80-89
90-99
100-109
Parts Cost ($)
Slide 37
Cumulative Distribution



The cumulative frequency distribution shows the
number of items with values less than or equal to the
upper limit of each class.
The cumulative relative frequency distribution shows
the proportion of items with values less than or equal
to the upper limit of each class.
The cumulative percent frequency distribution shows
the percentage of items with values less than or equal
to the upper limit of each class.
Slide 38
Example: Hudson Auto Repair

Cumulative Distributions
Cost ($)
< 59
< 69
< 79
< 89
< 99
< 109
Cumulative Cumulative
Cumulative
Relative
Percent
Frequency
Frequency
Frequency
2
.04
4
15
.30
30
31
.62
62
38
.76
76
45
.90
90
50
1.00
100
Slide 39
Ogive
An ogive is a graph of a cumulative distribution.
 The data values are shown on the horizontal axis.
 Shown on the vertical axis are the:
• cumulative frequencies, or
• cumulative relative frequencies, or
• cumulative percent frequencies
 The frequency (one of the above) of each class is
plotted as a point.
 The plotted points are connected by straight lines.

Slide 40
Example: Hudson Auto Repair
Ogive with Cumulative Frequencies
Cumulative Frequency

50
40
30
20
10
50
60
70
80
90
100
110
Parts
Cost ($)
Slide 41
Exploratory Data Analysis


The techniques of exploratory data analysis consist of
simple arithmetic and easy-to-draw pictures that can
be used to summarize data quickly.
One such technique is the stem-and-leaf display.
Slide 42
Stem-and-Leaf Display






This 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.
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 last
digit for each item in rank order.
Each line in the display is referred to as a stem.
Each digit on a stem is a leaf.
Slide 43
Example: Hudson Auto Repair

Stem-and-Leaf Display
5
6
7
8
9
10
2
2
1
0
1
1
7
2
1
0
3
4
2
2
2
7
5
2
2
3
7
5
5
3
5
7
9
6
4
8
8
7 8 8 8 9 9 9
4 5 5 5 6 7 8 9 9 9
9
9
Slide 44
Crosstabulations and Scatter Diagrams



Thus far we have focused on methods that are used
to summarize the data for one variable at a time.
Often a manager is interested in tabular and
graphical methods that will help understand the
relationship between two variables.
Crosstabulation and a scatter diagram are two
methods for summarizing the data for two variables
simultaneously.
Slide 45
Example: Finger Lakes Homes

Crosstabulation
The number of Finger Lakes homes sold for each
style and price for the past two years is shown below.
Price
Range
< $99,000
> $99,000
Total
Colonial
Home Style
Ranch Split A-Frame Total
18
12
6
14
19
16
12
3
55
45
30
20
35
15
100
Slide 46
Using Excel’s PivotTable Report
to Construct a Crosstabulation

Formula Worksheet (showing data entered)
1
2
3
4
5
6
7
8
9
A
B
Home Price ($)
1
>99K
2
<=99K
3
>99K
4
<=99K
5
<=99K
6
<=99K
7
>99K
8
>99K
C
Style
Colonial
Ranch
Ranch
A-Frame
Colonial
Split-Level
A-Frame
Colonial
D
E
Note: Rows 10-101 are not shown.
Slide 47
Using Excel’s PivotTable Report
to Construct a Crosstabulation

Changing the Default Order for the PivotTable Report
Step 1 Select the Tools pull-down menu
Step 2 Choose Options
Step 3 When the Options dialog box appears:
Select the Custom lists tab
In the List entries: box, type <= 99K and
press Enter, and type > 99K
Select Add
Select OK
Slide 48
Using Excel’s PivotTable Report
to Construct a Crosstabulation

Using the PivotTable Report
Step 1 Select the Data pull-down menu
Step 2 Choose the PivotTable and PivotChart Report
Step 3 When the PivotTable and PivotChart Wizard
Step 1 of 3 dialog box appears:
Choose Microsoft Excel list or database
Choose PivotTable
Select Next >
Step 4 When the PivotTable and PivotChart Wizard
Step 2 of 3 dialog box appears:
Enter A1:C101 in the Range box
Select Next >
Slide 49
Using Excel’s PivotTable Report
to Construct a Crosstabulation

Using the PivotTable Report
Step 5 When the PivotTable and PivotChart Wizard
Step 3 of 3 dialog box appears:
Select New Worksheet
Click on the Layout button
When the PivotTable and PivotChart
Wizard – Layout diagram appears:
Drag the Price ($) field button to the
ROW section of the diagram
Drag the Style field button to the
COLUMN section of the diagram
Slide 50
Using Excel’s PivotTable Report
to Construct a Crosstabulation

Using the PivotTable Report (Step 5 continued)
Drag the Home field button to the DATA
section of the diagram
Double click the Sum of Home field
button in the data section
When the PivotTable Field dialog box
appears:
Choose Count under Summarized by:
Select OK
Select OK
When the PivotTable and PivotChart Wizard
Step 3 of 3 dialog box reappears:
Select Finish>
Slide 51
Using Excel’s PivotTable Report
to Construct a Crosstabulation

D
1
2
3
4
5
6
7
8
Value Worksheet
E
F
G
H
I
J
Count of Home Style
Price ($)
Colonial Ranch Split-Level A-Frame Grand Total
<=99K
18
6
19
12
55
>99K
12
14
16
3
45
Grand Total
30
20
35
15
100
Slide 52
Example: Panthers Football Team

Scatter Diagram
The Panthers football team is interested in
investigating the relationship, if any, between
interceptions made and points scored.
x = Number of
Interceptions
1
3
2
1
3
y = Number of
Points Scored
14
24
18
17
27
Slide 53
Example: Panthers Football Team
Scatter Diagram
Number of Points Scored

y
30
25
20
15
10
5
0
0
1
2
3
Number of Interceptions
x
Slide 54
Using Excel’s Chart Wizard
to Construct a Scatter Diagram

Formula Worksheet (showing data entered)
1
2
3
4
5
6
7
A
Number of
Interceptions
1
3
2
1
3
B
Number of
Points Scored
14
24
18
17
27
C
Slide 55
Using Excel’s Chart Wizard
to Construct a Scatter Diagram

Producing a Scatter Diagram
Step 1 Select cells A1:B6
Step 2 Select the Chart Wizard
Step 3 When the Chart Type dialog box appears:
Choose XY (Scatter) in the Chart type list
Choose Scatter from the Chart sub-type
display
Select Next >
Step 4 When the Chart Source Data dialog box appears
Select Next >
… continued
Slide 56
Using Excel’s Chart Wizard
to Construct a Scatter Diagram

Producing a Scatter Diagram
Step 5 When the Chart Options dialog box appears:
Select the Titles tab and then
Delete Number of Points Scored in the
Chart title box
Enter Number of Interceptions in the Value
(X) axis box
Enter Number of Points Scored in the Value
(Y) axis box
Select the Legend tab and then
Remove the check in the Show Legend box
Select Next >
… continued
Slide 57
Using Excel’s Chart Wizard
to Construct a Scatter Diagram

Producing a Scatter Diagram
Step 6 When the Chart Location dialog box appears:
Specify the location for the new chart
Select Finish to display the scatter diagram
Slide 58
Using Excel’s Chart Wizard
to Construct a Scatter Diagram
Value Worksheet
A
8
9
10
11
12
13
14
15
16
17
18
19
20
B
C
Scatter Diagram
for the Panthers
30
Number of
Points Scored

20
10
0
0
1
2
3
4
Number of Interceptions
Slide 59
Tabular and Graphical Procedures
Data
Qualitative Data
Tabular
Methods
•Frequency
Distribution
•Rel. Freq. Dist.
•% Freq. Dist.
•Crosstabulation
Graphical
Methods
•Bar Graph
•Pie Chart
Quantitative Data
Tabular
Methods
•Frequency
Distribution
•Rel. Freq. Dist.
•Cum. Freq. Dist.
•Cum. Rel. Freq.
Distribution
•Stem-and-Leaf
Display
•Crosstabulation
Graphical
Methods
•Dot Plot
•Histogram
•Ogive
•Scatter
Diagram
Slide 60
End of Chapter 2
Slide 61