Statistics-for-business-and-economics-11th-edition-anderson-solutions-manual-190413050247 – 2 – 1 © – Studocu

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Chapter 2

Descriptive Statistics: Tabular and

Graphical Presentations

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. Learn how the shape of a data distribution is revealed by a histogram. Learn how to recognize when a
   data distribution is negatively skewed, symmetric, and positively skewed.

5. Be able to use and interpret the exploratory data analysis technique of a stem-and-leaf display.

6. Learn how to construct and interpret cross tabulations and scatter diagrams of bivariate data.

Statistics for Business and Economics 11th Edition Anderson Solutions Manual

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Solutions:

1. Class Frequency Relative Frequency
   A 60 60/120 = 0.
   B 24 24/120 = 0.
   C 36 36/120 = 0.
   120 1.

2. a. 1 – (.22 + .18 + .40) =.

b. .20(200) = 40

c/d.
Class Frequency Percent Frequency
A .22(200) = 44 22
B .18(200) = 36 18
C .40(200) = 80 40
D .20(200) = 40 20
Total 200 100

3. a. 360° x 58/120 = 174°

b. 360° x 42/120 = 126°

c.

Yes
48%

No Opinion
16%

No
35%

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d. CSI had the largest viewing audience. Desperate Housewives was in second place.

5. a.
   Name Frequency Relative Frequency Percent Frequency
   Brown 7 .14 14%
   Davis 6 .12 12%
   Johnson 10 .20 20%
   Jones 7 .14 14%
   Smith 12 .24 24%
   Williams 8 .16 16%
   50 1.

b.

0

2

4

6

8

10

12

14

Brown Davis Johnson Jones Smith Williams
Name

Frequency

c. Brown .14 x 360 = 50
Davis .12 x 360 = 43
Johnson .20 x 360 = 72
Jones .14 x 360 = 50
Smith .24 x 360 = 86
Williams .16 x 360 = 57

L&O
20%

CSI
36%

Trace
18%

Housewives
26%

Descriptive Statistics: Tabular and Graphical Presentations

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© 2010 Cengage Learning. All Rights Reserved.

d. Most common: Smith, Johnson and Williams

6. a.

Network Frequency Percent Frequency
ABC 15 30%
CBS 17 34%
FOX 1 2%
NBC 17 34%
Total 50 100%

0

2

4

6

8

10

12

14

16

18

ABC CBS FOX NBC

Network

Frequency

b. CBS and NBC are tied, each with 17 of the top rated television shows. ABC is a close third with 15.
The fact that the three networks are so close is surprising. FOX, the newest television network, does
not have the history to compete with the other three networks in term of the top rated shows in
television history.

Williams
16%

Brown
14%

Davis
12%
Johnson
20%

Jones
14%

Smith
24%

Descriptive Statistics: Tabular and Graphical Presentations

2 – 7

© 2010 Cengage Learning. All Rights Reserved.

b. Where do you live now?

What do you consider the ideal community?

c. Most adults are now living in a city (32%).

d. Most adults consider the ideal community a small town (30%).

e. Percent changes by living area: City -8%, Suburb -1%, Small Town +4%, and Rural Area +5%.
Suburb living is steady, but the trend would be that living in the city would decline while
living in small towns and rural areas would increase.

10. a.

Rating Frequency
Excellent 20
Good 101
Fair 528
Bad 244
Terrible 122
Total 1015

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b.

Rating

Percent
Frequency
Excellent 2
Good 10
Fair 52
Bad 24
Terrible 12
Total 100

c.

d. 24% + 12% = 36% of adults in the United Sates think the Federal Bank is doing a bad or a terrible
job in handling the credit problems. Only 10% + 2% = 12% think the Federal Bank is doing a good
or excellent job.

e. 40% + 10% = 50% of adults in Spain think the European Central Bank is doing a bad or terrible job
in handling the credit problems. Only 4% of adults in Spain think the European Central Bank is
doing a good or excellent job.

Both countries show pessimism and relatively low confidence in how the banks are handling the
credit problems in the financial markets. But in comparing the two countries, adults in Spain show
more concern and more pessimism about the bank’s ability compared to adults in the United States.

11. Class Frequency Relative Frequency Percent Frequency
    12 -14 2 0 5.
    15 -17 8 0 20.
    18 -20 11 0 27.
    21 -23 10 0 25.
    24 -26 9 0 22.
    Total 40 1 100.

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b/c.
Class Frequency Percent Frequency
6 – 7 4 20
8 – 9 2 10
10 – 11 8 40
12 – 13 3 15
14 – 15 3 15
20 100
15. a/b.
Waiting Time Frequency Relative Frequency
0 – 4 4 0.
5 – 9 8 0.
10 – 14 5 0.
15 – 19 2 0.
20 – 24 1 0.
Totals 20 1.

c/d.

Waiting Time Cumulative Frequency Cumulative Relative Frequency
Less than or equal to 4 4 0.
Less than or equal to 9 12 0.
Less than or equal to 14 17 0.
Less than or equal to 19 19 0.
Less than or equal to 24 20 1.

e. 12/20 = 0.

16. a.
    Salary Frequency
    150 -159 1
    160 -169 3
    170 -179 7
    180 -189 5
    190 -199 1
    200 -209 2
    210 -219 1
    Total 20

b.

Salary

Percent
Frequency
150 -159 5
160 -169 15
170 -179 35
180 -189 25
190 -199 5
200 -209 10
210 -219 5
Total 100

Descriptive Statistics: Tabular and Graphical Presentations

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c.

Salary

Cumulative Percent
Frequency
Less than or equal to 159 5
Less than or equal to 169 20
Less than or equal to 179 55
Less than or equal to 189 80
Less than or equal to 199 85
Less than or equal to 209 95
Less than or equal to 219 100
Total 100

d.

e. There is skewness to the right.

f. (3/20)(100) = 15%

17. a. The highest price stock is for IBM with a price of $107 per share.
    The lowest price stock is for Alcoa with a price of $11 per share.

b. A class size of 10 results in 10 classes.

Price per Share Frequency
$10-19 5
$20-29 10
$30-39 3
$40-49 2
$50-59 6
$60-69 2
$70-79 1
$80-89 0
$90-99 0
$100-109 1

Descriptive Statistics: Tabular and Graphical Presentations

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c. The distribution shows a positive skewness.

0

1

2

3

4

5

6

7

0-249 250-499 500-749 750-999 1000-

1249

1250-

1499

1500-

1759

1750-

1999

2000-

2249

Holiday Spending

Frequency

d. The holiday spending ranges from $0 to less than $2250. The majority of the spending is between
$250 and $1000 with 16 of the 25 customers, 64%, in this range. The middle or average spending is around
$750 per customer. The distribution has a positive skewness with two consumers above $1750. One consumer
is above $2000.

19. a/b/c/d.

Class
(Minutes)
Frequency

Relative
Frequency

Cumulative
Frequency

Cumulative Relative
Frequency
1-5 12 .60 12.
6- 10 3 .15 15.
11 -15 2 .10 17.
16 -20 1 .05 18.
21 -25 1 .05 19.
26 -30 0 .00 19.
31 -34 1 .05 20 1.

e.

f. 60% of office workers spend 5 minutes or less on unsolicited email and spam. However, 25% of
office workers spend more than 10 minutes per day on this task.

0

1

0 5 10 15 20 25 30 35
Time

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20. a.
    Off-Course Income Percent
    ($1000s) Frequency Frequency
    0-4,999 30 60
    5,000-9,999 9 18
    10,000-14,999 4 8
    15,000-19,999 0 0
    20,000-24,999 3 6
    25,000-29,999 2 4
    30,000-34,999 0 0
    35000 -39,999 0 0
    40,000-44,999 1 2
    45,000-49,999 0 0
    Over 50,000 1 2
    Total 50 100

b. Histogram of Off-Course Income

Note: The first class is labeled 5000 and provides the golfers who had an off-course income in the
range 0 to 4999 or less than 5000. These were the golfers with less than $5 million in off-course
income.

c. Off-course income is skewed to the right. Only Tiger Woods earns over $50 million.

d. Considering the top 50 golfers, the majority (60%) earn less than $5 million in off-course income per
year. 60% + 18% = 78% earn less than $10 million. Five golfers (10%) earn between $20 million
and $30 million. Tiger Woods with $99 million and Phil Mickelson with $40 million in off-
course income are clearly the leaders in this income category.

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• Chapter
  – 2 –
• 23. Leaf Unit =.
• 24. Leaf Unit =

Descriptive Statistics: Tabular and Graphical Presentations

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26. a. 100 shares at $50 per share

1 0 3 7 7
2 4 5 5
3 0 0 5 5 9
4 0 0 0 5 5 8
5 0 0 0 4 5 5

This stem-and-leaf display shows that the trading prices are closely grouped together. Rotating the
stem-and-leaf display counter clockwise shows a histogram that is slightly skewed to the left but is
roughly symmetric.

b. 500 shares traded online at $50 per share.

0 5 7
1 0 1 1 3 4
1 5 5 5 8
2 0 0 0 0 0 0
2 5 5
3 0 0 0
3 6
4
4
5
5
6 3

This stretched stem-and-leaf display shows that the distribution of online trading prices for most of
the brokers for 500 shares are lower than the trading prices for broker assisted trades of 100 shares.
There are a couple of outliers. York Securities charges $36 for an online trade and Investors National
charges much more than the other brokers: $62 for an online trade.

27. a.
    7 5 9
    8 3 6
    9 5 6 8
    10 0 4 4
    11 1 5
    12
    13 7
    14 5 5

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b.
y

x

A

B

C

100.

84.

16.

1

0.

15.

83.

2

100.

100.

100.

Total

c.
y

x

A

B

C

27.

61.

11.

100.

0.

16.

83.

100.

1 2

Total

d. 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.

–

–

–

8

24

40

56

-40 -30 -20 -10 0 10 20 30 40

x

y

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b. There is a negative relationship between x and y; y decreases as x increases.

31. a. Row Percentages:

Household Income ($1000s)
Education Level Under 25 25.0-49 50.0-74 75.0-99 100 or
More

Total

Not H. Graduate 42 34 13 5 3 100.
H. Graduate 22 31 22 11 12 100.
Some College 13 26 23 16 20 100.
Bachelor’s Degree 6 15 20 18 39 100.
Beyond Bach. Deg. 3 10 16 15 53 100.
Total 17 25 20 13 22 100.

There are six percent frequency distributions in this table with row percentages. The first five give
the percent frequency distribution of income for each educational level. The total row provides an
overall percent frequency distribution for household income.

The second row, labeled H. Graduate, is the percent frequency distribution for households headed
by high school graduates. The fourth row, labeled Bachelor’s Degree, is the percent frequency
distribution for households headed by bachelor’s degree recipients.

b. The percentage of households headed by high school graduates earning $75,000 or more is 11% +
12 = 24%. The percent of households headed by bachelor’s degree recipients earning $75,
or more is 18% + 39% = 57%.

c. The percent frequency histogram for high school graduates.