Chapter Nominal: Occupation, undergraduate major. Ordinal: Rating of university professor, Taste test ratings. Interval: age, income

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1 Chapter Nominal: Occupation, undergraduate major. Ordinal: Rating of university professor, Taste test ratings. Interval: age, income 2.2 a Interval b Nominal c. Nominal d Interval e Interval f Ordinal 2.3 a Interval b Ordinal c Nominal d Ordinal 2.4 a Interval b Nominal c Nominal 2.5 a Ordinal b Ordinal c Ordinal 2.6 a Interval b Interval c Nominal d Ordinal 2.7 a Interval b Nominal c Ordinal d Interval e Interval 2.8 a Interval 5

2 b Nominal c Nominal d Interval e Ordinal 2.9 a Interval b Interval c Nominal d Interval e Nominal 2.1 a Interval b Interval c Nominal d Ordinal e Interval 2.11 a Pie Chart Other 23% Unemployed 4% Manager 27% Blue-collar 7% Clerical 39% Most graduates are managers or are doing clerical work. 6

3 2.12a Bar Chart A B C D E Brand b Pie Chart E 9% A 3% D 35% C 1% B 16% c Brands A and D are most popular, but no one brand dominates the market. 7

4 2.13 Pie Chart Internet 11% Guide 31% Word 19% Dealer 39% Most consumers get their information from a dealer Pie Chart Number Community 5% 3% Career 11% Location 18% Reputation 37% Majors 26% Reputation and choice of majors dominate the responses. 8

5 2.15 Bar Chart Excellent Good Average Poor Unacceptable A large proportion of customers rate the facilities as average or better Bar Chart First Second Third Fourth Fifth Sixth Seventh Eighth The horse has had a satisfactory career, but not outstanding one. 9

6 2.17 Pie Chart Test 12% Medical 6% Analytical 4% Electronic 3% Computers 75% Most of HP s revenue comes from the sale of computers. 2.18a A bar chart is suitable for these results. A pie chart is incorrect. b Bar Chart Percent invested Less than $1, 1, to 19,999 2, to 29,999 3, to 39,999 4, to 49,999 5, to 79,999 Income group 8, to 99,999 1, to 25, Over 25, As income increases so does ownership of retirement savings plans. 1

7 2.19a Bar Chart Europe asia North America South America Africa b Pie Chart South America 7% Africa 5% Europe 17% North America 38% asia 33% Most immigrants come from North America (and Central America) and Asia. 11

8 2.2 We use a pie chart to depict the proportion of all firms with health insurance categorized by the size of the firm. Thus, 4% of all firms with health insurance have fewer than 1 employees. Pie Chart 1+ 15% 5 to 999 3% 1 to 499 9% <1 4% 25 to 99 15% 1 to 24 18% Bar Chart Percentage of all firms <1 to to 99 1 to to Firm size We use a bar chart to depict the proportion of firms in each size category that has health insurance. For example, 97.7% of firms with 1, or more employees have health insurance. 12

9 2.21 Pie Chart Taxes 41% Crude oil 42% Margin 7% Company 1% Canadians pay too much tax Pie Chart Duty 16% Distiller 19% GST 6% Sales tax 1% Markup 49% Canadians pay too much tax. 13

10 2.23a Bar Chart 3,, 2,5, 2,, 1,5, 1,, 5, Agriculture Mining Construction Manufacturing Transportation Wholesale Retail Finance Services Other b Pie Chart 8% 1% % 3% 2% 2% 2% 17% 56% 9% c Both charts indicate that the service and retail industry dominate. 14

11 2.24 a Reason Relative Sickness Death in family 6.6 Team Forgot 8.8 b Bar Chart Reasons 2.25a Degree BA 136 BBA 51 B Eng 3 B Sc 9 Other 31 b Bar Chart BA BBA Beng BSc Other Degree c 15

12 Pie Chart Other 13% BSc 4% Beng 1% BBA 22% BA 6% c Most applicants have the BA degree and about one-fifth have a BBA Bar Chart Austen Duval London Monroe Reardon Vote Monroe is the predicted winner in a tight race Pie Chart Drowsy 44% Stomach 32% Dizzy 5% heradache 19% Drowsiness and stomach upset are the two most common symptoms. 16

13 2.28 a Bar Chart IBM Compaq Dell Other Computer brand Pie Chart Other 26% IBM 21% Compaq 13% b Dell 4% c Dell is most popular with 4% proportion, followed by other, 26%, IBM, 21% and Compaq, 13%. 17

14 2.29 a Software Excel 34 Minitab 17 SAS 3 SPSS 4 Other 12 b Pie Chart Other 17% SPSS 6% SAS 4% Excel 49% Minitab 24% c Excel is the choice of about half the sample, one-quarter have opted for Minitab, and a small fraction chose SAS and SPSS. 2.3 Pie Chart Worse 12% Same 21% Better 67% 18

15 67% said the economy would get better, 21% said the same, and the rest stated that the economy would worsen , 12, or , 6, or a 7 to b Interval width = 2. 11(rounded to 2); upper limits: 9, 92, 94, 96, 98, 1, 12, 14, 16, a 7 to b Interval width = 4; upper limits: 28, 32, 36, 4, 44, 48, 52, a Histogram Time b The histogram is bimodal and negatively skewed a Histogram Speeds b The histogram is positively skewed. 19

16 2.37 a b A B C Stem & Leaf Display Stems Leaves 4->4 5-> > > > > >1145 Histogram Coupons c The distribution is approximately bell shaped and symmetric a 2

17 A B C Stem & Leaf Display Stems Leaves 19 -> > > > > > > > > >3 3 -> >2 b Histogram Time c The distribution is approximately bell shaped and slightly negatively skewed a A B C D Stem & Leaf Display Stems Leaves 4 -> > > > > >7 46 ->7 47 ->9 b 21

18 Histogram Times c The histogram is positively skewed. 2.4 a Histogram Stores b Ogive Stores c The number of stores is bimodal and positively skewed

19 Histogram Games The histogram is positively skewed a Histogram Rounds b Stem & Leaf Display c Stems Leaves -> > > > >2 Ogive Rounds d The histogram is symmetric (approximately) and bimodal

20 Histogram Marks c The histogram is negatively skewed, bimodal, and not bell shaped Histogram Lengths The histogram is unimodal, bell-shaped and roughly symmetric. Most of the lengths lie between 18 and 23 inches Histogram Copies The histogram is unimodal and positively skewed. On most days the number of copies made is between 2 and 1. On a small percentage of days more than 1 copies are made

21 Histogram Weights The histogram is unimodal, symmetric and bell-shaped. Most tomatoes weigh between 2 and 7 ounces with a small fraction weighing less than 2 ounces or more than 7 ounces Histogram Gallons The histogram is positively skewed and unimodal. Most households use between 2 and 45 gallons per day. The center of the distributions appears to be around 25 to 3 gallons Histogram Incomes The histogram is symmetric, unimodal, and bell shaped. 2.49a 25

22 Histogram Prices b Histogram 1% 5% % Rounds c A B C D E Stem & Leaf Display Stems Leaves -> > > > >2 d The histogram is positively skewed, unimodal, and not bell-shaped. We learn that most prices lie between 2 and 275 thousand dollars with a small number of houses selling for more than $275,. 2.5 Histogram Customers The histogram is unimodal and positively skewed The histogram should contain 9 or 1 bins. We chose 1. 26

23 b Histogram Times c The histogram is positively skewed. d The histogram is not bell-shaped Histogram Books The histogram of the number of books shipped daily is negatively skewed, It appears that there is a maximum number that the company can ship a Histogram Repaid b 27

24 Histogram Repaid c The scorecards appear to be relatively poor predictors a Histogram Repaid b Histogram Repaid d This scorecard is a much better predictor. 2.55a 28

25 Scatter Diagram 3 2 Returns Inflation b There is no sign of a linear relationship between inflation (the independent variable) and returns (the dependent variable). Common stocks do not provide a hedge against inflation Bar Chart M Engineering F M Physical sciences F Earth sciences M M M F F F Mathematics Computer sciences Biological sciences Doctorate M F Agriculture M F Social sciences M F Psychology F M The two bar charts are somewhat dissimilar. There is a weak relationship

26 Bar Chart 6, 5, 4, 3, 2, M W M W M W 1, Black Hispanic Asian + Minority The variables race and gender are only slightly related a Scatter Diagram Time Age b There is a weak positive linear relationship between age and time

27 Scatter Diagram Sales Size There is a strong positive linear relationship. 2.6 Bar Chart 14, 12, 1, 8, 6, 4, 2, M F F M M F M F Never Married Widowed Divorced Marital status Gender and marital status are unrelated. 2.61a 31

28 Scatter Diagram 3 25 Internet use Age b There does not appear to be a linear relationship Age Group Accident rate (per driver) Fatal accident rate (per 1, drivers) Under Over b Bar Chart Rates A F Under 2 F F A A A F F F F F A A A A ver 74 Age group 32

29 c The accident rate generally decreases as the ages increase. The fatal accident rate decreases until the over 74 age category where there is an increase. As drivers age they become less likely to be involved in an accident. As a result the fatal accident rate also decreases except for the over 74 age group. Perhaps because of other health issues older drivers are more likely than other drivers to die as a result of the accident a Age Group Injury Rate (per 1 accidents) Fatal injury rate (per accident) 2 or less or more b Bar Chart.25 K.2 Rates K K I K I K I K I K I K I K I I I. 2 or less or more Age group c Older drivers who are in accidents are more likely to be injured or killed. d Exercise 2.62 addressed the issue of accident rates, where in this exercise we consider the severity of accidents. 33

30 2.64 Scatter Diagram 2 Price of gasoline Price of crude There is a strong positive linear relationship between the prices of crude oil and gasoline Bar Chart 6 Count of Student University BA B Eng Bba Other Degree Degree There is a relationship between degree and university. 34

31 2.66a Scatter Diagram Electricity Occupants 1 b There is moderately strong positive linear relationship between the number of occupants and electricity use Scatter Diagram Tickets Temperature There is a moderately strong positive linear relationship between temperature and the number of tickets. 35

32 2.68 Bar Chart 7 Count of Owner Last Last Purchase Second-last There is a relationship between the last two purchases. There is some brand loyalty Scatter Diagram Reading Speed Education There is a moderately strong linear relationship between years of education and reading speed. 36

33 2.7 a Scatter Diagram Income Height b There is a no linear relationship between the two variables Bar Chart 8 Count of Respondent Parent Do not smoke Smoke Smoke? Smoke? The two nominal variables are strongly correlated. 37

34 2.72 Scatter Diagram 3 CEO compensation Profit Scatter Diagram 3 CEO compensation year share return There does not appear to be a linear relationship between profit and CEO compensation or between 3-year share return and CEO compensation. 38

35 2.73 Line Charts Subscribers Year There has been a steady growth in subscribers over the ten-year period Line Chart Costs Year Costs have increased dramatically and appear to be accelerating. 39

36 2.75a Line Chart 5 4 Deficit Year b Deficits began falling after the sixth year (1991), approached in year 15( 2) and started rising again Line Chart Number of violent crimes 15, 14, 13, 12, 11, Year After rising for 3 years, the number of crimes has steadily decreased until year 12, where is started to rise again. 4

37 2.77 Line Chart Percentage Month There is some month-to-month fluctuation, but the percentage was only slightly lower after 24 months Line Charts 3. Number of Policies Individual Group Year The number of individual policies has been stable while group policies are increasing. 41

38 2.79a Line Chart 2 15 Exports Month b Line Chart 25 2 Imports Month 42

39 c Line Chart Balance Month d Trade between the two countries has increased exponentially. However, imports from Canada have increased at a faster rate than exports to Canada. 2.8a Line Chart Rate Month b There was a large decrease over the first half of the period, but has leveled since. 43

40 2.81 Line Charts 5 Number of degrees (1,s) Male Female Total Year There has been a gradual increase over the 18-year period. 2.82a Line Chart Sales Week b There has been a gradual weekly increase in sales

41 Line Chart GDP ($billions) Quarter The quarterly figures have grown exponentially Line Chart 2 Miles per gallon Year Gas mileage has steadily improved over the past 31 years. 45

42 2.85 Line Chart Exports Quarter Exports have steadily increased until quarter 41, at which point it leveled off Line Chart DJIA Month The trend until month 7 (1982) was slow but steady. Then the index grew exponentially until month 9, (1999), at which point there was a significant decrease and recovery. 46

43 2.87 Scatter Diagram Precious metal return 14% 12% 1% 8% 6% 4% 2% % -2% % 2% 4% 6% 8% 1% 12% 14% -4% -6% Inflation There is a weak linear relationship between inflation rate and precious metal returns Scatter DiagramPrice/gallon 2 Price of gasoline CPI There is a moderately strong linear relationship suggesting that the some of the price increase is due to inflation. 47

44 2.89 Pie Chart Very good 1% Excellent 3% Poor 15% Fair 27% Good 45% Most of the responses rate the food as good or fair. 2.9 Scatter DiagramIQ Twin 2 IQ Twin IQ Twin 1 There is a moderately strong linear relationship between the IQs of twins. 48

45 2.91 Histogram Crashes The histogram is positively skewed. Most computer users have less 25 crashes per 12 week period Although there are year-to-year fluctuations the winning time appears to be constant. Line Chart Winning time Year 49

46 2.93 Scatter Diagram Winning time Temperature There is a strong positive linear relationship between temperature and winning times. This explains some of the fluctuations in the line chart in Exercise Scatter Diagram Winning time Temperature 2.94 There is a moderately strong positive linear relationship between temperature and winning time. 5

47 Pie Chart Manual 18% Compute 44% Computer& manual 38% 2.95 The most popular approach is to use the computer exclusively, closely followed by a combination of manual calculations and computer solutions. Would be statistics textbook authors are recommended to write books that combine both approaches. 2.96a Scatter Diagram Son's height Father's height b The direction is positive. c There does appear to be a linear relationship. 51

48 2.97 Histogram More Books Most students borrowed no books Canada Pie Chart Other 11% Yahoo 15% MSN 12% Google 62% 52

49 U.S. Pie Chart Other 18% Google 36% Yahoo 3% In Canada Google is the most popular by a wide margin. In the United States Google and Yahoo are the leaders. MSN 16% 2.99a Line Chart Exports Month 53

50 b Line Chart Imports Month c Line Chart 2 Balance Month d Imports to Japan and exports from Japan have grown over the past 28 years. However, imports have grown much more quickly. 54

51 2.1 Line Chart 2.5 American dollar Month The value of the American dollar has risen over the years Scatter Diagram 35 3 Time Score There is a moderately strong linear relationship between time and score. 55

52 2.12 Line Chart Participation Year The participation rate varies between 5 and 6%. Line Chart 25 2 Revenues Year 2.13 Growth in revenues has increased exponentially. 56

53 2.14 Pie Chart Strongly agree 4% Strongly disagree 15% Agree 23% Disagree 2% Neither 38% Most students would not agree. 2.15a Line Chart 12 1 Exports Month 57

54 b Line Chart Imports Month c Line Chart 1 Balance Month d Trade has been increasing but imports have increased faster than exports to Mexico. 58

55 2.16 Scatter Diagram Credit Debit There is a moderately strong negative linear relationship Histogram w The histogram is almost bell shaped (slightly bimodal). Many people gain between 1 and 35 pounds. 59

56 2.18 Bar Chart 1 Count of Driver 9 Ask 8 Continue Map Continue Response 3 2 Ask Other Map Other 1 Male Female Gender Gender There are large differences between male and female responses. There is a strong relationship between gender and what drivers do when lost

57 Line Chart U.S. Dollar Month The US dollar increased in value until month 176 (1985), decreases until month 251(1991), rose again until month 376 (22), and then fell sharply Histogram Vocabulary Most vocabularies lie between 16 and 28 words

58 Bar Chart 5 Count of Customer 45 4 V good Good Good Excellent Fair V good Rate 15 Fair Poor 1 5 Poor Excellent Children No children Children? Children The rating and whether the children of customers accompanied them are related Histogram Pay Most directors earned between $25, and $55,. 62

59 2.113 Histogram More Meetings Most directors attended less than 13 meetings Fatal accidents Line Chart Fatal accidents Year Passenger deaths 63

60 Line Chart Passenger deaths Year Safety has not improved using the number of passenger deaths. However, using the number of fatal accidents, safety has improved Bar Chart Income Tax rate Australia Britain France Germany Hungary Ireland Italy Japan Country Mexico Norway Spain Sweden Switzerland United States 39.6 All countries, except Switzerland set their highest income tax rate at about 4% or higher. 64

61 2.116 Line Chart 5 4 PE Ratio Month The average PE ratio appears to lie between 5 and 25 except for two periods, just before the 1929 stock market crash and in the 199 s Business Statistics course (Example 2.6) Scatter Diagram 1 8 Calculus Marks 65

62 Mathematical Statistics course (Example 2.7) Scatter Diagram 1 8 Calculus Marks There appears to be a stronger linear relationship between marks in the mathematical statistics course and calculus than the relationship between the marks in the business statistics course and the marks in calculus Business Statistics course (Example 2.6) Scatter Diagram 1 8 Marks Midterm marks 66

63 Mathematical Statistics course (Example 2.7) Scatter Diagram 1 8 Marks Midterm marks The relationship between midterm marks and final marks appear to be similar for both statistics courses a A B C D E F G Count of ID number Area Gender Grand Total Grand Total

64 Bar Chart 45 4 Count of ID number Acct Mktg 35 3 Acct Finance 25 2 Finance GM GM Mktg Area 15 Other Other 1 5 Female male Gender Gender Males and females differ in their areas of employment. Females tend to choose accounting marketing/sales and males opt for finance. b A B C D E Count of ID number Satisfaction Area Very Quite Little None Grand Total Acct Finance GM Mktg Other Grand Total F 68

65 Bar Chart 4 Count of ID number Quite Very 2 15 Very Little Quite Very Very Quite Little Quite Satisfaction 1 5 Quite Little Little None Little Very None None None Acct Finance GM Mktg Other Area Area Area and job satisfaction are related. Graduates who work in finance and general management appear to be more satisfied than those in accounting, marketing/sales, and others. c Scatter Diagram Search Salary There is no linear relationship between salary and the time needed to land a job. 69

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