Statistics for International Business School, Hanze University of Applied Science, Groningen, The Netherlands

1. IBS Statistics Year 1 Dr. Ning DING n.ding@pl.hanze.nl I.007

2. What we are going to learn? Whytheyfailed in STA1? Chapter 1: Whatisstatistics? Why? What? Types of statistics, variables Levels of measurement Chapter 2: Describing data Frequency tables Frequency distributions Graphicpresentation

3. Summary of the reasons 1. Why Failed in Statistics? 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement Absent for the lessons; Didn’t do the home assignments; Ignore the EXCEL lessons; 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Cannotuse the theoriesflexibly; Keep misconceptions and misunderstandingtill the exam; Overestimateself and underestimate the subject.

4. 1. Why Failed in Statistics? Statistics are everywhere. CPP BPP BRM 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

5. 1. Why Failed in Statistics? Statistics help you make decisions. 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

6. 1. Why Failed in Statistics? Statistics help you make decisions. Making decisions 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement Interpret data Present data 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Analyze data Organize data Collect data

7. 1. Why Failed in Statistics? Statistics help you make decisions. Statistics: The science of collecting, organizing, presenting, analyzing and interpreting data to assist in making more effective decisions. 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Descriptive Statistics: Methods of organizing, summarizing and presenting data in an informative way. Inferential Statistics: Methods used to estimate a property of a population on the basis of a sample.

8. 1. Why Failed in Statistics? Statistics help you make decisions. Descriptive Statistics: Inferential Statistics: 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Population: The entire set of individual or objects of interest or the measurements obtained from all individuals or objects of interest. Sample: A portion, or part, of the population of interest.

9. 1. Why Failed in Statistics? Statistics help you make decisions. Inferential Statistics: 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Population: The entire set of individual or objects of interest or the measurements obtained from all individuals or objects of interest. Sample: A portion, or part, of the population of interest.

10. Types of variables 1. Why Failed in Statistics? Qualitative: nonnumeric, attribute 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Quantitative: numerical

11. Types of variables 1. Why Failed in Statistics? 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Qualitative Quantitative

12. Types of variables 1. Why Failed in Statistics? Discrete counting 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement Continuous measuring Discrete Continuous Discrete Continuous Height 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Salary ClassSize

15. Because of the relative values, the data classified can be ranked or ordered. 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

16. Levels of Measurement 1. Why Failed in Statistics? Nominal: 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement No logical order Ordinal: 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Ranked or ordered

19. Differences and ratios are meaningful for this level of measurement. 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

20. Levels of Measurement 1. Why Failed in Statistics? Salary 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement Interval: Ratio: Interval: Ratio: IQ Temperature Distance 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

21. Levels of Measurement 1. Why Failed in Statistics? 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

22. Levels of Measurement 1. Why Failed in Statistics? 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

24. The driverswhoreceived a speeding ticket Kansas City last month.

25. Thoseon welfare in Cook County (Chicago), Illinois.

26. The 30 stocks reported as a part of the Dow Jones Industrial Average. Sample Population 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Population Sample P14. N.4 Ch.1

28. Determin the level of measurementforeach of the variables. 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation township all the rest… Township = nominal level All the rest…=ratio P18. N.16 Ch.1

31. Exercises 2-a 1. Why Failed in Statistics? A total of 1,000 residents in Minnesotawereaskedwhichseasontheypreferred. The resultswere 100 liked winter best, 300 liked spring, 400 likedsummer, and 200 likedfall. If the data weresummarized in a frequencytable, howmany classes wouldbeused? Whatwouldbe the relativefrequenciesforeachclass? 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation P27. N.3 .Ch.2

33. The class frequencies on the vertical axis

34. The class frequencies are proportional to the heights of the bars.2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation RelativeFrequency 5/12 = 41.67% 3/12=25.00% 4/12=33.33% Total 12

36. GraphicPresentation of Qualitativedata 1. Why Failed in Statistics? Piechartsrequirethatyouinclude all the categoriesthatmake up a whole. Usethemonlywhenyou want to emphasizeeachcategory'srelation to the whole. 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

39. Step 2: Class Interval Step 1: Just enough recipe 2 to the k rule 10 -< 20 4 20 -< 30 1 30 -< 40 10 40 -< 50 9 50 -< 60 3 N=27 1. Why Failed in Statistics? Frequency Distribution: 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement N=27 number of class=5 22=4 23=8 24=16 25=32 26=64 27=128  (55-14)/5 ≈ 8 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Step 3: Choose nice “round” boundaries Step 4: Try to avoid empty and open classes

40. Exercises 2-b > $30 - $0 i = 5 1. Why Failed in Statistics? 6 A set of data consists of 45 observationsbetween $0 and $29. Whatsizewouldyourecommendfor the class interval? 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 25 = 32, 26 = 64, suggests 6 classes 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Use interval of 5 P33. N.8 .Ch.2

41. Exercises 2-b 99 - 51 5 1. Why Failed in Statistics? i > ≈ 9 The QuickChange Oil Company has a number of outlets in the metropolitanSeattlearea. The dailynumber of oilchanges at the Oak Street outlet in the past 20 days are: 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 98 55 62 79 59 51 90 72 56 70 62 66 80 94 79 63 73 71 85 a. Howmanyclasseswouldyourecommend? a. 24 = 16, 25 = 32, suggests 5 classes 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation b. Whatclass interval wouldyousuggest? b. Use interval of 10 P34. N.12.Ch.2

42. Exercises 2-b 1. Why Failed in Statistics? The QuickChange Oil Company has a number of outlets in the metropolitanSeattlearea. The dailynumber of oilchanges at the Oak Street outlet in the past 20 days are: 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 98 55 62 79 59 51 90 72 56 70 62 66 80 94 79 63 73 71 85 c. Whatlower limit wouldyourecommendfor the firstclass? 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation c. 50 P34. N.12.Ch.2

44. The class frequencies on the vertical axis

45. The class frequencies are represented by the heights of the bars and the bars are adjacent to each other. 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

47. Similar to a histogram3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Not floating in the air

48. GraphicPresentation of Quantitative data 1. Why Failed in Statistics? c) Cumulative frequency distribution: used to determine how many or what proportion of the data values are below or above a certain value. 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Notfloating in the air

49. Why Failed in Statistics? 1. Why Failed in Statistics? 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

50. GraphicPresentation of Quantitative data 1. Why Failed in Statistics? c) Cumulative frequency distribution: used to determine how many or what proportion of the data values are below or above a certain value. 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation Notfloating in the air

51. Whatwe have learnt? 1. Why they failed in Statistics? 2. Chapter 1: What is Statistics? Why? What? Types of statistics, variables Levels of measurement 3. Chapter 2: Describing Data Frequency tables Frequency distributions Graphic presentation

52. Exercises 1-a Whatis the level of measurement for each of the following variables? A. student IQ ratings B. distance studentstravel to class C. student scores on the first statistics test D. a classification of students by state of birth E. a ranking of students as freshmen, sophomore, junior, and senior F. Number of hoursstudentsstudy per week Interval Ratio Interval Nominal Ordinal Ratio

53. Exercises 1-b Place these variables in the following classification tables. Salary Gender Sales volumen of MP3 players Soft drink preference Temperature SAT scores Student rank in class Rating of a finance professor Number of home computers Discrete Continuous b. Gender d. Soft drink preference Qualitative f. SAT scores a. Salary g. Student rank in class c. Sales volume of MP3 players Quantitative e. Temperature h. Rating of a finance professor i. Number of home computers P16. N.9 Ch.1

54. Exercises 1-c Place these variables in the following classification tables. Salary Gender Sales volumen of MP3 players Soft drink preference Temperature SAT scores Student rank in class Rating of a finance professor Number of home computers Discrete Continuous b. Gender Nominal d. Soft drink preference Ordinal g. Student rank in class h. Rating of a finance professor f. SAT scores e. Temperature Interval a. Salary Ratio c. Sales volume of MP3 players i. Number of home computers

55. Exercises 1-d The tablebelow reports the number of cars and light trucks soldby the Big Three automobile manufacturersforJune 2004 and June 2005. 1. Compare the totalsales in the twomonths. What do youconclude? Has there been anincrease in sales? (1,056,144-866,243) 866,243 Total salesincreased 189,901 units or 21.9%. P17. N.13 Ch.1

56. Exercises 1-d The tablebelow reports the number of cars and light trucks soldby the Big Three automobile manufacturersforJune 2004 and June 2005. 2. Compare the percent of the Big Threemarketforeachcompany. Did the marketincreaseordid GM stealsalesfrom the othercompanies? Citeevidence. GM increased the market share by 9 percentage points from 43% to 52%. Crysler lost 3% and Ford lost 6%. All three companies increased the nubmer of units sold. P17. N.13 Ch.1

57. FrequencyDistribution Example: Dr. Tillman is Dean of the School of Business Socastee University. He wishes to prepare a report showing the number of hours per week students spend studying. He selects a random sample of 30 students and determines the number of hours each student studied last week. 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Step 1: Just enough recipe 2 to the k rule Select the smallest number (k) for the number of classes such that 2k is greater than the number of observations (n).

59. 21=2; 22=4; 23=8; 24=16; 25=32; 26=64; 27=128; 28=256; 29=512; 210=1024 …

60. The rule suggest 10 classes.

61. If sample size (n) = 80

62. 21=2; 22=4; 23=8; 24=16; 25=32; 26=64; 27=128; …

63. The rule suggest 7 classes.Sample size (n) = 30 21=2; 22=4; 23=8; 24=16; 25=32; 26=64; 27=128; … The rule suggest 5 classes.

65. The classes must be mutually exclusive and exhaustive.Class interval (next unit of Highest value – lowest value) / number of classes. Usually we will chose some convenient number as class interval that satisfy the inequality.

67. Lowest value = 10.3 hours

68. k=5.

69. Hence, class interval ≥ (33.9-10.3)/5 ≈ 4.7

71. Lowest value = 10.3 hours.

72. Range = nu of highest – lowest = 23.5.

73. K=5; Interval = 5.

74. With k=5 and interval = 5, the classes will cover a range of 25.

75. Let’s split the surplus in the lower and upper tail equally. (25-23.5)/2 = 0.75. Hence, the lower limit of the first class should be around (10.3 – 0.75)=9.55 and upper limit of the last class should be (33.8 + 0.75)=34.55.

76. 9.55 and 34.55 look odd. Some convenient and close numbers would be 10 and 35.“10 up to 15” means the interval from 10 to 15 that includes 10 but not 15.

77. FrequencyDistribution Step 4: Tally the data 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Example: Hours studying 7 10 up to 15 12 15 up to 20 20 up to 25 7 25 up to 30 3 30 up to 35 1

78. FrequencyDistribution 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Step 5: Count the number

79. FrequencyDistribution 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6. Relative Frequency Distribution Step 5: Count the number

80. Exercises 2-b A set of data consists of 38 observations. Howmany classes wouldyourecommendfor the frequency distribution? 25 = 32, 26 = 64, therefore, 6 classes A set of data consists of 230 observationsbetween $235 and $567. Whatclass interval wouldyourecommend. 27 = 128, 28 = 256, suggests 8 classes Classintervals of 40, 45, or 50 all wouldbeacceptable. P33. N.7 .Ch.2