Chapter 2
Descriptive Statistics: Tabular and
Graphical Methods
Learning Objectives
1.
Learn how to construct and interpret summarization procedures for qualitative data such as :
frequency and relative frequency distributions, bar graphs and pie charts.
2.
Learn how to construct and interpret tabular summarization procedures for quantitative data such as:
frequency and relative frequency distributions, cumulative frequency and cumulative relative
frequency distributions.
3.
Learn how to construct a dot plot, a histogram, and an ogive as graphical summaries of quantitative
data.
4.
Be able to use and interpret the exploratory data analysis technique of a stem-and-leaf display.
5.
Learn how to construct and interpret cross tabulations and scatter diagrams of bivariate data.
2-1
Chapter 2
2-2
Descriptive Statistics: Tabular and Graphical Methods
Solutions:
1.
Class
A
B
C
2.
a.
1 - (.22 + .18 + .40) = .20
b.
.20(200) = 40
Frequency
60
24
36
120
Relative Frequency
60/120 = 0.50
24/120 = 0.20
36/120 = 0.30
1.00
c/d
Class
A
B
C
D
Total
3.
a.
360° x 58/120 = 174°
b.
360° x 42/120 = 126°
Frequency
.22(200) = 44
.18(200) = 36
.40(200) = 80
.20(200) = 40
200
Percent Frequency
22
18
40
20
100
c.
No
Opinion
16.7%
Yes
48.3%
No
35%
2-3
Chapter 2
d.
70
60
Frequency
50
40
30
20
10
0
Yes
No
No Opinion
Response
4.
a.
The data are qualitative.
b.
TV Show
Millionaire
Frasier
Chicago Hope
Charmed
Total:
Frequency
24
15
7
4
50
2-4
Percent
Frequency
48
30
14
8
100
Descriptive Statistics: Tabular and Graphical Methods
c.
30
Frequency
25
20
15
10
5
0
Millionaire
Frasier
Chicago
Charmed
TV Show
Charmed
8%
Chicago
14%
Millionaire
48%
Frasier
30%
d.
5.
Millionaire has the largest market share. Frasier is second.
a.
Major
Management
Accounting
Finance
Marketing
Total
Relative Frequency
55/216 = 0.25
51/216 = 0.24
28/216 = 0.13
82/216 = 0.38
1.00
2-5
Percent Frequency
25
24
13
38
100
Chapter 2
b.
90
80
Frequency
70
60
50
40
30
20
10
0
Management
Accounting
Finance
Major
c.
6.
Pie Chart
a.
Book
7 Habits
Millionaire
Motley
Dad
WSJ Guide
Frequency
10
16
9
13
6
2-6
Percent Frequency
16.66
26.67
15.00
21.67
10.00
Marketing
Descriptive Statistics: Tabular and Graphical Methods
Other
Total:
6
60
10.00
100.00
The Ernst & Young Tax Guide 2000 with a frequency of 3, Investing for Dummies with a frequency
of 2, and What Color is Your Parachute? 2000 with a frequency of 1 are grouped in the "Other"
category.
b.
The rank order from first to fifth is: Millionaire, Dad, 7 Habits, Motley, and WSJ Guide.
c.
The percent of sales represented by The Millionaire Next Door and Rich Dad, Poor Dad is 48.33%.
7.
Rating
Outstanding
Very Good
Good
Average
Poor
Frequency
19
13
10
6
2
50
Relative Frequency
0.38
0.26
0.20
0.12
0.04
1.00
Management should be pleased with these results. 64% of the ratings are very good to outstanding.
84% of the ratings are good or better. Comparing these ratings with previous results will show
whether or not the restaurant is making improvements in its ratings of food quality.
8.
a.
Position
Pitcher
Catcher
1st Base
2nd Base
3rd Base
Shortstop
Left Field
Center Field
Right Field
9.
Frequency
17
4
5
4
2
5
6
5
7
55
b.
Pitchers (Almost 31%)
c.
3rd Base (3 - 4%)
d.
Right Field (Almost 13%)
e.
Infielders (16 or 29.1%) to Outfielders (18 or 32.7%)
Relative Frequency
0.309
0.073
0.091
0.073
0.036
0.091
0.109
0.091
0.127
1.000
a/b.
Starting Time
7:00
7:30
8:00
8:30
9:00
Frequency
3
4
4
7
2
20
2-7
Percent Frequency
15
20
20
35
10
100
Chapter 2
c.
Bar Graph
8
7
Frequency
6
5
4
3
2
1
0
7:00
7:30
8:00
8:30
9:00
Starting Time
d.
9:00
10%
7:00
15%
7:30
20%
8:30
35%
8:00
20%
e.
10. a.
The most preferred starting time is 8:30 a.m.. Starting times of 7:30 and 8:00 a.m. are next.
The data refer to quality levels of poor, fair, good, very good and excellent.
b.
Rating
Poor
Fair
Good
Very Good
Excellent
Frequency
2
4
12
24
18
60
2-8
Relative Frequency
0.03
0.07
0.20
0.40
0.30
1.00
Descriptive Statistics: Tabular and Graphical Methods
c.
Bar Graph
30
Frequency
25
20
15
10
5
0
Poor
Fair
Good
Very Good
Excellent
Rating
Pie Chart
d.
The course evaluation data indicate a high quality course. The most common rating is very good
with the second most common being excellent.
11.
Class
Frequency
Relative Frequency
Percent Frequency
12-14
15-17
18-20
21-23
24-26
2
8
11
10
9
0.050
0.200
0.275
0.250
0.225
5.0
20.0
27.5
25.5
22.5
2-9
Chapter 2
Total
40
1.000
100.0
12.
Class
less than or equal to 19
less than or equal to 29
less than or equal to 39
less than or equal to 49
less than or equal to 59
Cumulative Frequency
10
24
41
48
50
Cumulative Relative Frequency
.20
.48
.82
.96
1.00
13.
18
16
Frequency
14
12
10
8
6
4
2
0
10-19
20-29
30-39
40-49
50-59
1.0
.8
.6
.4
.2
0
10
20
30
2 - 10
40
50
60
Descriptive Statistics: Tabular and Graphical Methods
14. a.
b/c.
Class
6.0 - 7.9
8.0 - 9.9
10.0 - 11.9
12.0 - 13.9
14.0 - 15.9
Frequency
4
2
8
3
3
20
Percent Frequency
20
10
40
15
15
100
15. a/b.
Waiting Time
0-4
5-9
10 - 14
15 - 19
20 - 24
Totals
Frequency
4
8
5
2
1
20
Relative Frequency
0.20
0.40
0.25
0.10
0.05
1.00
c/d.
Waiting Time
Less than or equal to 4
Less than or equal to 9
Less than or equal to 14
Less than or equal to 19
Less than or equal to 24
e.
Cumulative Frequency
4
12
17
19
20
Cumulative Relative Frequency
0.20
0.60
0.85
0.95
1.00
12/20 = 0.60
16. a.
Stock Price ($)
10.00 - 19.99
20.00 - 29.99
30.00 - 39.99
40.00 - 49.99
50.00 - 59.99
60.00 - 69.99
Total
Relative
Frequency
0.40
0.16
0.24
0.08
0.04
0.08
1.00
Frequency
10
4
6
2
1
2
25
2 - 11
Percent
Frequency
40
16
24
8
4
8
100
Chapter 2
12
Frequency
10
8
6
4
2
0
10.0019.99
20.0029.99
30.0039.99
40.0049.99
50.0059.99
60.0069.99
Stock Price
Many of these are low priced stocks with the greatest frequency in the $10.00 to $19.99 range.
b.
Earnings per
Share ($)
-3.00 to -2.01
-2.00 to -1.01
-1.00 to -0.01
0.00 to 0.99
1.00 to 1.99
2.00 to 2.99
Total
Relative
Frequency
0.08
0.00
0.08
0.36
0.36
0.12
1.00
Frequency
2
0
2
9
9
3
25
2 - 12
Percent
Frequency
8
0
8
36
36
12
100
Descriptive Statistics: Tabular and Graphical Methods
10
Frequency
9
8
7
6
5
4
3
2
1
0
-3.00 to
-2.01
-2.00 to
-1.01
-1.00 to
-0.01
0.00 to
0.99
1.00 to
1.99
2.00 to
2.99
Earnings per Share
The majority of companies had earnings in the $0.00 to $2.00 range. Four of the companies lost
money.
17.
Call Duration
2 - 3.9
4 - 5.9
6 - 7.9
8 - 9.9
10 - 11.9
Totals
Frequency
5
9
4
0
2
20
Relative Frequency
0.25
0.45
0.20
0.00
0.10
1.00
Histogram
10
Frequency
9
8
7
6
5
4
3
2
1
0
2.0 - 3.9
4.0 - 5.9
6.0 - 7.9
Call Duration
2 - 13
8.0 - 9.9
10.0 - 11.9
Chapter 2
18. a.
Lowest salary: $93,000
Highest salary: $178,000
b.
Salary
($1000s)
91-105
106-120
121-135
136-150
151-165
166-180
Total
Relative
Frequency
0.08
0.10
0.22
0.36
0.18
0.06
1.00
Frequency
4
5
11
18
9
3
50
c.
Proportion $135,000 or less: 20/50.
d.
Percentage more than $150,000: 24%
Percent
Frequency
8
10
22
36
18
6
100
20
18
16
Frequency
14
12
10
8
6
4
2
0
91-105
106-120 121-135 136-150 151-165 166-180
Salary ($1000s)
e.
19. a/b.
Number
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
Totals
Frequency
2
7
3
6
1
1
20
2 - 14
Relative Frequency
0.10
0.35
0.15
0.30
0.05
0.05
1.00
Descriptive Statistics: Tabular and Graphical Methods
c/d.
.
Number
Less than or equal to 149
Less than or equal to 159
Less than or equal to 169
Less than or equal to 179
Less than or equal to 189
Less than or equal to 199
Cumulative Frequency
2
9
12
18
19
20
Cumulative Relative Frequency
0.10
0.45
0.60
0.90
0.95
1.00
e.
Frequency
20
15
10
5
140
20. a.
160
180
200
The percentage of people 34 or less is 20.0 + 5.7 + 9.6 + 13.6 = 48.9.
b.
The percentage of the population that is between 25 and 54 years old inclusively is
13.6 + 16.3 + 13.5 = 43.4
c.
The percentage of the population over 34 years old is
16.3 + 13.5 + 8.7 + 12.6 = 51.1
d.
The percentage less than 25 years old is 20.0 + 5.7 + 9.6 = 35.3.
So there are (.353)(275) = 97.075 million people less than 25 years old.
e.
An estimate of the number of retired people is (.5)(.087)(275) + (.126)(275) = 46.6125 million.
21. a/b.
Computer
Usage (Hours)
0.0 2.9
3.0 5.9
6.0 8.9
9.0 - 11.9
12.0 - 14.9
Total
Frequency
5
28
8
6
3
50
2 - 15
Relative
Frequency
0.10
0.56
0.16
0.12
0.06
1.00
Chapter 2
c.
30
Frequency
25
20
15
10
5
0
0.0 - 2.9
3.0 - 5.9
6.0 - 8.9
9.0 - 11.9 12.0 - 14.9
Computer Usage (Hours)
d.
e.
The majority of the computer users are in the 3 to 6 hour range. Usage is somewhat skewed toward
the right with 3 users in the 12 to 15 hour range.
2 - 16
Descriptive Statistics: Tabular and Graphical Methods
22.
23.
Leaf Unit = 0.1
24.
Leaf Unit = 10
2 - 17
Chapter 2
25.
26.
Leaf Unit = 0.1
0
4 7 8 9 9
1
1 2 9
2
0 0 1 3 5 5 6 8
3
4 9
4
8
5
6
7
1
2 - 18
Descriptive Statistics: Tabular and Graphical Methods
27.
2 - 19
Chapter 2
28. a.
0
5 8
1
1 1 3 3 4 4
1
5 6 7 8 9 9
2
2 3 3 3 5 5
2
6 8
3
3
6 7 7 9
4
0
4
7 8
5
5
6
0
b.
2000 P/E
Forecast
5-9
10 - 14
15 - 19
20 - 24
25 - 29
30 - 34
35 - 39
40 - 44
45 - 49
50 - 54
55 - 59
60 - 64
Total
Frequency
2
6
6
6
2
0
4
1
2
0
0
1
30
29. a.
2 - 20
Percent
Frequency
6.7
20.0
20.0
20.0
6.7
0.0
13.3
3.3
6.7
0.0
0.0
3.3
100.0
Descriptive Statistics: Tabular and Graphical Methods
y
x
1
2
Total
A
5
0
5
B
11
2
13
C
2
10
12
Total
18
12
30
1
2
Total
A
100.0
0.0
100.0
B
84.6
15.4
100.0
C
16.7
83.3
100.0
b.
y
x
c.
y
x
d.
1
2
A
27.8
0.0
B
61.1
16.7
C
11.1
83.3
Total
100.0
100.0
Category A values for x are always associated with category 1 values for y. Category B values for x
are usually associated with category 1 values for y. Category C values for x are usually associated
with category 2 values for y.
30. a.
2 - 21
Chapter 2
56
40
y
24
8
-8
-24
-40
-40
-30
-20
-10
0
10
20
30
40
x
b.
There is a negative relationship between x and y; y decreases as x increases.
31.
Quality Rating
Good
Very Good
Excellent
Total
Meal Price ($)
20-29
30-39
33.9
2.7
54.2
60.5
11.9
36.8
100.0
100.0
10-19
53.8
43.6
2.6
100.0
40-49
0.0
21.4
78.6
100.0
As the meal price goes up, the percentage of high quality ratings goes up. A positive relationship
between meal price and quality is observed.
32. a.
Sales/Margins/ROE
A
B
C
D
E
Total
0-19
20-39
EPS Rating
40-59
1
1
3
4
1
4
1
2
4
0-19
20-39
1
6
60-79
1
5
2
1
80-100
8
2
3
9
13
60-79
11.11
41.67
28.57
20.00
80-100
88.89
16.67
42.86
Total
9
12
7
5
3
36
b.
Sales/Margins/ROE
A
B
C
D
E
EPS Rating
40-59
8.33
14.29
60.00
33.33
14.29
20.00
66.67
33.33
Total
100
100
100
100
100
Higher EPS ratings seem to be associated with higher ratings on Sales/Margins/ROE. Of those
companies with an "A" rating on Sales/Margins/ROE, 88.89% of them had an EPS Rating of 80 or
2 - 22
Descriptive Statistics: Tabular and Graphical Methods
higher. Of the 8 companies with a "D" or "E" rating on Sales/Margins/ROE, only 1 had an EPS
rating above 60.
33. a.
Sales/Margins/ROE
A
B
C
D
E
Total
A
1
1
1
1
4
Industry Group Relative Strength
B
C
D
2
2
4
5
2
3
3
2
1
1
1
2
11
7
10
E
Total
9
12
7
5
3
36
1
1
2
4
b/c. The frequency distributions for the Sales/Margins/ROE data is in the rightmost column of the
crosstabulation. The frequency distribution for the Industry Group Relative Strength data is in the
bottom row of the crosstabulation.
d.
Once the crosstabulation is complete, the individual frequency distributions are available in the
margins.
34. a.
80
Relative Price Strength
70
60
50
40
30
20
10
0
0
20
40
60
80
100
120
EPS Rating
b.
One might expect stocks with higher EPS ratings to show greater relative price strength. However,
the scatter diagram using this data does not support such a relationship.
The scatter diagram appears similar to the one showing "No Apparent Relationship" in Figure 2.19.
35. a.
2 - 23
Chapter 2
900.0
800.0
Gaming Revenue
700.0
600.0
500.0
400.0
300.0
200.0
100.0
0.0
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
Hotel Revenue
b.
There appears to be a positive relationship between hotel revenue and gaming revenue. Higher
values of hotel revenue are associated with higher values of gaming revenue.
36. a.
Vehicle
F-Series
Silverado
Taurus
Camry
Accord
Total
b.
Frequency
17
12
8
7
6
50
Percent Frequency
34
24
16
14
12
100
The two top selling vehicles are the Ford F-Series Pickup and the Chevrolet Silverado.
2 - 24
800.0
Descriptive Statistics: Tabular and Graphical Methods
Accord
12%
F-Series
34%
Camry
14%
Taurus
16%
Silverado
24%
c.
37. a/b.
Industry
Beverage
Chemicals
Electronics
Food
Aerospace
Totals:
Frequency
2
3
6
7
2
20
2 - 25
Percent Frequency
10
15
30
35
10
100
Chapter 2
8
7
Frequency
6
5
4
3
2
1
0
Beverage
Chemicals Electronics
Food
Aerospace
Industry
c.
38. a.
Movie
Blair Witch Project
Phantom Menace
Beloved
Primary Colors
Truman Show
Total
Frequency
159
89
85
57
51
441
Percent Frequency
36.0
20.2
19.3
12.9
11.6
100.0
b.
Truman
12%
Colors
13%
Witch
36%
Beloved
19%
Phantom
20%
2 - 26
Descriptive Statistics: Tabular and Graphical Methods
c.
The percent of mail pertaining to 1999 cover stories is 36.0 + 20.2 = 56.2%
39. a-d.
Sales
0 - 499
500 - 999
1000 - 1499
1500 - 1999
2000 - 2499
Total
Relative
Frequency
0.65
0.15
0.00
0.15
0.05
1.00
Frequency
13
3
0
3
1
20
Cumulative
Frequency
13
16
16
19
20
Cumulative
Relative
Frequency
0.65
0.80
0.80
0.95
1.00
e.
14
12
Frequency
10
8
6
4
2
0
0-499
500-999
1000-1499
1500-1999
Sales
40. a.
Closing Price
0 - 9 7/8
10 - 19 7/8
20 - 29 7/8
30 - 39 7/8
40 - 49 7/8
50 - 59 7/8
60 - 69 7/8
70 - 79 7/8
Totals
Frequency
9
10
5
11
2
2
0
1
40
2 - 27
Relative Frequency
0.225
0.250
0.125
0.275
0.050
0.050
0.000
0.025
1.000
2000-2499
Chapter 2
b.
Closing Price
Less than or equal to 9 7/8
Less than or equal to 19 7/8
Less than or equal to 29 7/8
Less than or equal to 39 7/8
Less than or equal to 49 7/8
Less than or equal to 59 7/8
Less than or equal to 69 7/8
Less than or equal to 79 7/8
Cumulative Frequency
9
19
24
35
37
39
39
40
Cumulative Relative Frequency
0.225
0.475
0.600
0.875
0.925
0.975
0.975
1.000
c.
12
Frequency
10
8
6
4
2
0
5
15
25
35
45
55
65
75
Closing Price
d.
Over 87% of common stocks trade for less than $40 a share and 60% trade for less than $30 per
share.
41. a.
Exchange
American
New York
Over the Counter
Frequency
3
2
15
20
Relative
Frequency
0.15
0.10
0.75
1.00
b.
Earnings Per
Share
0.00 - 0.19
0.20 - 0.39
0.40 - 0.59
0.60 - 0.79
Frequency
7
7
1
3
2 - 28
Relative
Frequency
0.35
0.35
0.05
0.15
Descriptive Statistics: Tabular and Graphical Methods
0.80 - 0.99
2
0.10
20
1.00
Seventy percent of the shadow stocks have earnings per share less than $0.40. It looks like low EPS
should be expected for shadow stocks.
Price-Earning
Ratio
0.00 - 9.9
10.0 - 19.9
20.0 - 29.9
30.0 - 39.9
40.0 - 49.9
50.0 - 59.9
Frequency
3
7
4
3
2
1
20
Relative
Frequency
0.15
0.35
0.20
0.15
0.10
0.05
1.00
P-E Ratios vary considerably, but there is a significant cluster in the 10 - 19.9 range.
42.
Income ($)
18,000-21,999
22,000-25,999
26,000-29,999
30,000-33,999
34,000-37,999
Total
Frequency
13
20
12
4
2
51
Relative
Frequency
0.255
0.392
0.235
0.078
0.039
1.000
25
Frequency
20
15
10
5
0
18,000 - 21,999
22,000 - 25,999
26,000 - 29,999
Per Capita Income
2 - 29
30,000 - 33,999
34,000 - 37,999
Chapter 2
43. a.
b/c/d.
Number Answered
Correctly
5-9
10 - 14
15 - 19
20 - 24
25 - 29
30 - 34
Totals
e.
Relative
Frequency
0.050
0.200
0.375
0.225
0.075
0.075
1.000
Frequency
2
8
15
9
3
3
40
Cumulative
Frequency
2
10
25
34
37
40
Relatively few of the students (25%) were able to answer 1/2 or more of the questions correctly. The
data seem to support the Joint Council on Economic Education’s claim. However, the degree of
difficulty of the questions needs to be taken into account before reaching a final a conclusion.
44. a/b.
High Temperature
Low Temperature
3
3
9
4
4
3 6 8
5
7
5
0 0 0 2 4 4 5 5 7 9
6
1 4 4 4 4 6 8
6
1 8
7
3 5 7 9
7
2 4 5 5
8
0 1 1 4 6
8
9
0 2 3
9
c.
It is clear that the range of low temperatures is below the range of high temperatures. Looking at the
stem-and-leaf displays side by side, it appears that the range of low temperatures is about 20 degrees
below the range of high temperatures.
d.
There are two stems showing high temperatures of 80 degrees or higher. They show 8 cities with
high temperatures of 80 degrees or higher.
2 - 30
Descriptive Statistics: Tabular and Graphical Methods
e.
Frequency
High Temp.
Low. Temp.
0
1
0
3
1
10
7
2
4
4
5
0
3
0
20
20
Temperature
30-39
40-49
50-59
60-69
70-79
80-89
90-99
Total
Low Temperature
45. a.
80
75
70
65
60
55
50
45
40
35
30
40
50
60
70
80
90
100
High Temperature
b.
There is clearly a positive relationship between high and low temperature for cities. As one goes up
so does the other.
46. a.
Occupation
Cabinetmaker
Lawyer
Physical Therapist
Systems Analyst
Total
30-39
40-49
1
5
1
2
7
Satisfaction Score
50-59 60-69 70-79
2
4
3
2
1
1
5
2
1
1
4
3
10
11
8
30-39
40-49
Satisfaction Score
50-59 60-69 70-79
80-89
1
3
Total
10
10
10
10
40
80-89
Total
2
b.
Occupation
2 - 31
Chapter 2
Cabinetmaker
Lawyer
Physical Therapist
Systems Analyst
c.
10
50
20
20
20
50
10
40
10
20
40
30
10
10
30
10
20
100
100
100
100
Each row of the percent crosstabulation shows a percent frequency distribution for an occupation.
Cabinet makers seem to have the higher job satisfaction scores while lawyers seem to have the
lowest. Fifty percent of the physical therapists have mediocre scores but the rest are rather high.
47. a.
40,000
35,000
Revenue $mil
30,000
25,000
20,000
15,000
10,000
5,000
0
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
Employees
b.
There appears to be a positive relationship between number of employees and revenue. As the
number of employees increases, annual revenue increases.
48. a.
Fuel Type
Year Constructed Elec Nat. Gas Oil Propane Other
1973 or before
40
183
12
5
7
1974-1979
24
26
2
2
0
1980-1986
37
38
1
0
6
1987-1991
48
70
2
0
1
Total 149
317
17
7
14
Total
247
54
82
121
504
b.
Year Constructed
1973 or before
1974-1979
1980-1986
1987-1991
Total
Frequency
247
54
82
121
504
Fuel Type
Electricity
Nat. Gas
Oil
Propane
Other
Total
2 - 32
Frequency
149
317
17
7
14
504
100,000
Descriptive Statistics: Tabular and Graphical Methods
c.
Crosstabulation of Column Percentages
Fuel Type
Year Constructed Elec Nat. Gas Oil Propane Other
1973 or before
26.9
57.7
70.5
71.4
50.0
1974-1979
16.1
8.2
11.8
28.6
0.0
1980-1986
24.8
12.0
5.9
0.0
42.9
1987-1991
32.2
22.1
11.8
0.0
7.1
Total 100.0 100.0 100.0 100.0 100.0
d.
Crosstabulation of row percentages.
Year Constructed
1973 or before
1974-1979
1980-1986
1987-1991
e.
Fuel Type
Elec Nat. Gas Oil Propane Other
16.2
74.1
4.9
2.0
2.8
44.5
48.1
3.7
3.7
0.0
45.1
46.4
1.2
0.0
7.3
39.7
57.8
1.7
0.0
0.8
Total
100.0
100.0
100.0
100.0
Observations from the column percentages crosstabulation
For those buildings using electricity, the percentage has not changed greatly over the years. For the
buildings using natural gas, the majority were constructed in 1973 or before; the second largest
percentage was constructed in 1987-1991. Most of the buildings using oil were constructed in 1973
or before. All of the buildings using propane are older.
Observations from the row percentages crosstabulation
Most of the buildings in the CG&E service area use electricity or natural gas. In the period 1973 or
before most used natural gas. From 1974-1986, it is fairly evenly divided between electricity and
natural gas. Since 1987 almost all new buildings are using electricity or natural gas with natural gas
being the clear leader.
49. a.
Crosstabulation for stockholder's equity and profit.
Stockholders' Equity ($000)
0-1200
1200-2400
2400-3600
3600-4800
4800-6000
Total
b.
0-200
10
4
4
200-400
1
10
3
18
2
16
Profits ($000)
400-600
600-800
3
1
3
6
1
2
800-1000
1000-1200
1
2
1
1
1
2
4
4
Total
12
16
13
3
6
50
800-1000
1000-1200
Total
Crosstabulation of Row Percentages.
Stockholders' Equity ($1000s)
0-200
200-400
2 - 33
Profits ($000)
400-600
600-800
Chapter 2
0-1200
1200-2400
2400-3600
3600-4800
4800-6000
c.
50. a.
83.33
25.00
30.77
0.00
51. a.
0.00
0.00
7.69
0.00
16.67
0.00
12.50
7.69
33.33
0.00
8.33
0.00
7.69
66.67
0.00
0-300
23
4
27
Profit ($1000s)
300-600
600-900
4
4
2
2
1
1
2
2
1
13
6
900-1200
4
Total
27
12
4
4
3
50
900-1200
0.00
16.67
25.00
25.00
0.00
Total
100
100
100
100
100
2
1
1
Crosstabulation of Row Percentages.
Market Value ($1000s)
0-8000
8000-16000
16000-24000
24000-32000
32000-40000
c.
0.00
0.00
23.08
0.00
50.00
Stockholder's equity and profit seem to be related. As profit goes up, stockholder's equity goes up.
The relationship, however, is not very strong.
Crosstabulation of market value and profit.
Market Value ($1000s)
0-8000
8000-16000
16000-24000
24000-32000
32000-40000
Total
b.
8.33
62.50
23.08
0.00
33.33
0-300
85.19
33.33
0.00
0.00
0.00
Profit ($1000s)
300-600
600-900
14.81
0.00
33.33
16.67
50.00
25.00
25.00
50.00
66.67
33.33
There appears to be a positive relationship between Profit and Market Value. As profit goes up,
Market Value goes up.
Scatter diagram of Profit vs. Stockholder's Equity.
2 - 34
100
100
100
100
100
Descriptive Statistics: Tabular and Graphical Methods
1400.0
1200.0
Profit ($1000s)
1000.0
800.0
600.0
400.0
200.0
0.0
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
Stockholder's Equity ($1000s)
b.
52. a.
Profit and Stockholder's Equity appear to be positively related.
Scatter diagram of Market Value and Stockholder's Equity.
2 - 35
6000.0
7000.0
Chapter 2
45000.0
Market Value ($1000s)
40000.0
35000.0
30000.0
25000.0
20000.0
15000.0
10000.0
5000.0
0.0
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
6000.0
Stockholder's Equity ($1000s)
b.
There is a positive relationship between Market Value and Stockholder's Equity.
2 - 36
7000.0