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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 1 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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Descriptive Statistics: Tabular and Graphical Presentations
2 - 2 © 2012 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 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 48.3% No Opinion 16.7% No 35.0%
Descriptive Statistics: Tabular and Graphical Presentations 2 - 3 © 2012 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. 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 10 20 30 40 50 60 70 Yes No No Opinion Frequency Response 0 2 4 6 8 10 12 14 16 18 20 L&O CSI Trace Housewives Frequency TV Show
d. CSI had the largest viewing audience. Desperate Housewives was in second place.
Presentations 2 - 4 © 2012 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
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
5. a.
Frequency Name L&O 20% CSI 36% Trace 18% Housewives 26%
Brown Davis Johnson Jones Smith Williams
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
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.
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Descriptive Statistics: Tabular and Graphical Presentations 2
5 © 2012
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 Frequency Network Williams 16% Brown 14% Davis 12% Johnson 20% Jones 14% Smith 24%
Management should be very pleased with the survey results. 40% + 46% = 86% of the ratings are very good to excellent. 94% of the ratings are good or better. This does not look to be a Delta flight where significant changes are needed to improve the overall customer satisfaction ratings.
b. While the overall ratings look fine, note that one customer (2%) rated the overall experience with the flight as Fair and two customers (4%) rated the overall experience with the flight as Poor. It might be insightful for the manager to review explanations from these customers as to how the flight failed to meet expectations. Perhaps, it was an experience with other passengers that Delta could do little to correct or perhaps it was an isolated incident that Delta could take steps to correct in the future.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 6 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 7. a. Rating Frequency Percent Frequency Excellent 20 40 Very Good 23 46 Good 4 8 Fair 1 2 Poor 2 4 50 100
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
Pitchers (Almost 31%)
3rd Base (3 - 4%)
Right Field (Almost 13%) 0 5 10 15 20 25 30 35 40 45 50 Poor Fair Good Very Good Excellent Percent Frequency Customer Rating
8. a.
b.
c.
d.
e. Infielders (16 or 29.1%) to Outfielders (18 or 32.7%)
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%).
Descriptive Statistics: Tabular and Graphical Presentations 2 - 7 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
9. a.
0% 5% 10% 15% 20% 25% 30% 35% City Suburb Small Town Rural Area Percent Living Area 0% 5% 10% 15% 20% 25% 30% 35% City Suburb Small Town Rural Area Percent Living Area Living Area Live Now Ideal Community City 32% 24% Suburb 26% 25% Small Town 26% 30% Rural Area 16% 21% Total 100% 100%
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.
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 8 © 2012 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. a. Rating Frequency Excellent 20 Good 101 Fair 528 Bad 244 Terrible 122 Total 1015 b. Rating Percent Frequency Excellent 2 Good 10 Fair 52 Bad 24 Terrible 12 Total 100 c.
0 10 20 30 40 50 60 Terrible Bad Fair Good Excellent Percent Frequency Rating
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 9 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
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
11.
12.
Descriptive Statistics: Tabular and Graphical Presentations
2 - 10 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 14. a. 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 .2 .4 .6 .8 0 10 20 30 40 50 1.0 60
Descriptive Statistics: Tabular and Graphical Presentations 2 - 11 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 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 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. 0 1 2 3 4 5 6 7 8 150-159 160-169 170-179 180-189 190-199 200-209 210-219 Frequency Salary
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 $109 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.
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 12 ©
Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2012
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 c
0 2 4 6 8 10 12 $10-19 $20-29 $30-39 $40-49 $50-59 $60-69 $70-79 $80-89 $90-99 $100-109 Frequency Price per Share
18.
a. The lowest holiday spending is $180; the highest $2050.
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 13 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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
b.
Relative Cumulative Cumulative Relative Revenue Frequency Frequency Frequency Frequency 0-49 6 .12 6 .12 50-99 29 .58 35 .70 100-149 11 .22 46 .92 150-199 0 .00 46 .92 200-249 1 .02 47 .94 250-299 1 .02 48 .96 300-349 0 .00 48 .96 350-399 0 .00 48 .96 400-449 2 .04 50 1.00 Total 50 1.00 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 Frequency Holiday Spending
19. a/b/c/d.
e. The majority of the large corporations (40) have revenues in the $50 billion to $149 billion range. Only 4 corporations have revenues of over $200 billion and only 2 corporations have revenues over $400 billion. .70, or 70%, of the corporations have revenues under $100 billion. .30, or 30%, of the corporations have revenues of $100 billion or more.
f.
The histogram shows the distribution is skewed to the right with four corporations in the $200 to $449 billion range.
g. Exxon-Mobil is America’s largest corporation with an annual revenue of $443 billion. Walmart is the second largest corporation with an annual revenue of $406 billion. All other corporations have annual revenues less than $300 billion. Most (92%) have annual revenues less than $150 billion.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 14 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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 0 5 10 15 20 25 30 35 0-49 50-99 100-149 150-199 200-249 250-299 300-349 350-399 400-449 Frequency Revenue (Billion $)
20. a.
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 $99.8 million and Phil Mickelson with $40.2 million in offcourse income are clearly the leaders in this income category.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 15 © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
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 0 5 10 15 20 25 30 35 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 Over 50,000 Frequency Income Limit for Each Class ($1000s)
21.
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 16 © 2012 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.
d.
22. 5 7 8 6 4 5 8 7 0 2 2 5 5 6 8 8 0 2 3 5 0 5 10 15 20 25 30 0-2.9 3-5.9 6-8.9 9-11.9 12-14.9 Frequency Computer Usage (Hours)
The median pay for these careers is generally in the $70 and $80 thousands. Only four careers have a median pay of $100 thousand or more. The highest median pay is $121 thousand for a finance director.
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 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 26. Median Pay 6 6 7 7 7 2 4 6 7 7 8 9 8 0 0 1 3 7 9 9 10 0 6 11 0 12 1
Descriptive Statistics: Tabular and Graphical Presentations 2 - 17
The most frequent top pay is in the $130 thousand range. However, the top pay is rather evenly distributed between $100 and $160 thousand. Two unusually high top pay values occur at $214 thousand for a finance director and $221 thousand for an investment banker. Also, note that the top pay has more variability than the median pay.
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.
Descriptive Statistics: Tabular and Graphical Presentations 2 -
May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Top Pay 10 0 6 9 11 1 6 9 12 2 5 6 13 0 5 8 8 14 0 6 15 2 5 7 16 17 18 19 20 21 4 22 1
18 © 2012 Cengage Learning. All Rights Reserved.
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. 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.
Descriptive Statistics: Tabular and Graphical Presentations 2 - 19 © 2012 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 - 20 © 2012 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 y x Modern Business Statistics with Microsoft Office Excel 4th Edition Anderson Solutions Manual Full Download: http://testbanktip.com/download/modern-business-statistics-with-microsoft-office-excel-4th-edition-anderson-solutions-manual/ Download all pages and all chapters at: TestBankTip.com
