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.
2 - 1 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Statistics for Business and Economics 11th Edition Anderson Solutions Manual Full Download: http://testbanktip.com/download/statistics-for-business-and-economics-11th-edition-anderson-solutions-manual/ Download all pages and all chapters at: TestBankTip.com
Chapter 2 2 - 2 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Solutions: 1. Class Frequency Relative Frequency A 60 60/120 = 0.50 B 24 24/120 = 0.20 C 36 36/120 = 0.30 120 1.00 2. a. 1 - (.22 + .18 + .40) = .20
.20(200) = 40
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
a. 360° x 58/120 = 174°
360° x
= 126°
Yes 48.3% No Opinion 16.7% No 35.0%
b.
c/d.
3.
b.
42/120
c.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 3 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. d. 0 10 20 30 40 50 60 70 Yes No No Opinion Response Frequency 4. a. Categorical b. TV Show Frequency Percent Frequency Law & Order 10 20% CSI 18 36% Without a Trace 9 18% Desperate Housewives 13 26% Total: 50 100% 0 2 4 6 8 10 12 14 16 18 20 L&O CSI Trace Housewives TV Show Frequency
d. CSI had the largest viewing audience. Desperate Housewives was in second place.
Chapter 2 2 - 4 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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 1.00 b. 0 2 4 6 8 10 12 14
Name Frequency c. Brown .14 x 360 = 50.4 Davis .12 x 360 = 43.2 Johnson .20 x 360 = 72.0 Jones .14 x 360 = 50.4 Smith .24 x 360 = 86.4 Williams .16 x 360 = 57.6 L&O 20% CSI 36% Trace 18% Housewives 26%
Brown Davis Johnson Jones Smith Williams
d. Most common: Smith, Johnson and Williams
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 5 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
Williams
Brown
Davis
Johnson
Jones
Smith
16%
14%
12%
20%
14%
24%
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.
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%)
Chapter 2 2 - 6 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Rating Frequency Relative Frequency Outstanding 19 0.38 Very Good 13 0.26 Good 10 0.20 Average 6 0.12 Poor 2 0.04 50 1.00
7.
Position Frequency Relative Frequency Pitcher 17 0.309 Catcher 4 0.073 1st Base 5 0.091 2nd Base 4 0.073 3rd Base 2 0.036 Shortstop 5 0.091 Left Field 6 0.109 Center Field 5 0.091 Right Field 7 0.127 55 1.000
8. a.
Living Area Live Now Ideal Community City 32% 24% Suburb 26% 25% Small Town 26% 30% Rural Area 16% 21% Total 100% 100%
9. a.
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 7 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
10.
Rating Frequency Excellent 20 Good 101 Fair 528 Bad 244 Terrible 122 Total 1015
a.
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.
Chapter 2 2 - 8 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. b. Rating Percent Frequency Excellent 2 Good 10 Fair 52 Bad 24 Terrible 12 Total 100
c.
Class Frequency Relative Frequency Percent Frequency 12-14 2 0.050 5.0 15-17 8 0.200 20.0 18-20 11 0.275 27.5 21-23 10 0.250 25.0 24-26 9 0.225 22.5 Total 40 1.000 100.0
11.
Statistics: Tabular and Graphical Presentations 2 - 9 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 12. Class Cumulative Frequency Cumulative Relative Frequency less than or equal to 19 10 .20 less than or equal to 29 24 .48 less than or equal to 39 41 .82 less than or equal to 49 48 .96 less than or equal to 59 50 1.00 13. 0 2 4 6 8 10 12 14 16 18 10-19 20-29 30-39 40-49 50-59 Frequency .2 .4 .6 .8 0 10 20 30 40 50 1.0 60 14. a.
Descriptive
Chapter 2 2 - 10 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. b/c. Class Frequency Percent Frequency 6.0 - 7.9 4 20 8.0 - 9.9 2 10 10.0 - 11.9 8 40 12.0 - 13.9 3 15 14.0 - 15.9 3 15 20 100 15. a/b. Waiting Time Frequency Relative Frequency 0 - 4 4 0.20 5 - 9 8 0.40 10 - 14 5 0.25 15 - 19 2 0.10 20 - 24 1 0.05 Totals 20 1.00 c/d. Waiting Time Cumulative Frequency Cumulative Relative Frequency Less than or equal to 4 4 0.20 Less than or equal to 9 12 0.60 Less than or equal to 14 17 0.85 Less than or equal to 19 19 0.95 Less than or equal to 24 20 1.00 e. 12/20 = 0.60 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
17.
e. There is skewness to the right.
f. (3/20)(100) = 15%
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 11 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
c.
d.
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
The general shape of the distribution is skewed to the right. Half of the companies (15) have a price per share less than $30. A mid-priced stock appears to be in the $30 to $49 range, while the most frequently priced stock is in the $20 to $29 range.
Five stocks are less than $20 per share (Alcoa, Bank of America, General Electric, Intel and Pfizer). Four stocks are $60 or more per share (3M, Chevron, ExxonMobil and IBM).
d. A variety of comparisons are possible depending upon when the study is done.
18. a. The lowest holiday spending is $180; the highest $2050.
b.
Chapter 2 2 - 12 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. c.
Spending Frequency Percent 0-249 3 12 250-499 6 24 500-749 5 20 750-999 5 20 1000-1249 3 12 1250-1499 1 4 1500-1759 0 0 1750-1999 1 4 2000-2249 1 4 Total 25 100
c The distribution shows a positive skewness.
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.
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.
2 - 13 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Descriptive Statistics: Tabular and Graphical Presentations
0 1 2 3 4 5 6 7 0-249 250-499 500-749 750-999 10001249 12501499 15001759 17501999 20002249 Holiday Spending Frequency
19. a/b/c/d. Class (Minutes) Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency 1-5 12 .60 12 .60 6-10 3 .15 15 .75 11-15 2 .10 17 .85 16-20 1 .05 18 .90 21-25 1 .05 19 .95 26-30 0 .00 19 95 31-34 1 .05 20 1.00
e.
0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 30 35 Time
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 $99.8 million and Phil Mickelson with $40.2 million in offcourse income are clearly the leaders in this income category.
Chapter 2 2 - 14 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 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
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 14.9 hour range.
2 - 15 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 21. a/b. Computer Usage (Hours) Frequency Relative Frequency 0.0 - 2.9 5 0.10 3.0 - 5.9 28 0.56 6.0 - 8.9 8 0.16 9.0 - 11.9 6 0.12 12.0 - 14.9 3 0.06 Total 50 1.00 c. 0 5 10 15 20 25 30 0-2.9 3-5.9 6-8.9 9-11.9 12-14.9 Computer Usage (Hours) Frequency
Descriptive Statistics: Tabular and Graphical Presentations
d.
Chapter 2 2 - 16 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 22. 5 7 8 6 4 5 8 7 0 2 2 5 5 6 8 8 0 2 3 5 23. Leaf Unit = .1 6 3 7 5 5 7 8 1 3 4 8 9 3 6 10 0 4 5 11 3 24. Leaf Unit = 10 11 6 12 0 2 13 0 6 7 14 2 2 7 15 5 16 0 2 8 17 0 2 3 25. 9 8 9 10 2 4 6 6 11 4 5 7 8 8 9 12 2 4 5 7 13 1 2 14 4 15 1
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.
500 shares traded online at $50 per share.
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: $62.50 for an online trade.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 17 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 26. a.
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
100 shares 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
b.
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
b. Observations such as the following can be made using the stem-and-leaf display.
The daily rate varies from $75 to $145
Typical mid-priced daily rates are $95 to $115 with the average daily rate around $100.
A daily rate in excess of $115 should be considered relatively high. High daily rates of $137 and $145 were found at three ski resorts.
b. Most frequent age group: 40-44 with 9 runners
c. 43 was the most frequent age with 5 runners
d. 4/40 = 10% of the runners were “20-something.” With only 10% of the registrants “20-something,” the article pointed out that surprisingly few registrants were in this age group. One suggested reason was that “20-somethings” don’t have the time to train for a 13.1 mile race. For “20-somethings,” college, starting careers, and starting families may take priority over training for long distance races.
Chapter 2
2 - 18 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
28. a. 2 1 4 2 6 7 3 0 1 1 1 2 3 3 5 6 7 7 4 0 0 3 3 3 3 3 4 4 4 6 6 7 9 5 0 0 0 2 2 5 5 6 7 9 6 1 4 6 6 7 2
29. a. y x A B C 5 11 2 0 2 10 12 18 5 13 12 30 Total 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
Descriptive Statistics: Tabular and Graphical Presentations 2 - 19 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. b. y x A B C 100.0 84.6 16.7 1 0.0 15.4 83.3 2 100.0 100.0 100.0 Total c. y x A B C 27.8 61.1 11.1 100.0 0.0 16.7 83.3 100.0 1 2 Total
30. a. -40 -24 -8 8 24 40 56 -40 -30 -20 -10 0 10 20 30 40 x y
b. There is a negative relationship between x and y; y decreases as x increases.
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.S. 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 11.93% + 12.07 = 24.00%. The percent of households headed by bachelor's degree recipients earning $75,000 or more is 18.72% + 39.02% = 57.74%.
c. The percent frequency histogram for high school graduates.
Chapter 2 2 - 20 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website,
or
in whole
in part.
a.
Household Income ($1000s) Education Level Under 25 25.0-49.9 50.0-74.9 75.0-99.9 100 or More Total Not H.S. Graduate 42.23 34.73 13.94 5.41 3.68 100.00 H.S. Graduate 22.25 31.00 22.75 11.93 12.07 100.00 Some College 13.99 26.20 23.31 16.20 20.30 100.00 Bachelor's Degree 6.42 15.19 20.66 18.72 39.02 100.00 Beyond Bach. Deg. 3.71 10.60 16.29 15.87 53.54 100.00 Total 17.77 25.08 20.64 13.90 22.62 100.00
31.
Row Percentages:
Statistics for Business and Economics 11th Edition Anderson Solutions Manual Full Download: http://testbanktip.com/download/statistics-for-business-and-economics-11th-edition-anderson-solutions-manual/ Download all pages and all chapters at: TestBankTip.com
