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# Lesson01

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

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1. 1. IBS Statistics<br />Year 1<br />Dr. Ning DING <br />n.ding@pl.hanze.nl<br />I.007<br />
2. 2. What we are going to learn?<br />Whytheyfailed in STA1?<br />Chapter 1: Whatisstatistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />Chapter 2: Describing data<br />Frequency tables<br />Frequency distributions<br />Graphicpresentation<br />
3. 3. Summary of the reasons<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />Absent for the lessons;<br />Didn’t do the home assignments;<br />Ignore the EXCEL <br />lessons;<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Cannotuse the theoriesflexibly;<br />Keep misconceptions and misunderstandingtill the exam;<br />Overestimateself and underestimate the subject.<br />
4. 4. 1. Why Failed in <br />Statistics?<br />Statistics are everywhere.<br />CPP<br />BPP<br />BRM<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
5. 5. 1. Why Failed in <br />Statistics?<br />Statistics help you make decisions.<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
6. 6. 1. Why Failed in <br />Statistics?<br />Statistics help you make decisions.<br />Making decisions<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />Interpret data<br />Present data<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Analyze data<br />Organize data<br />Collect data<br />
7. 7. 1. Why Failed in <br />Statistics?<br />Statistics help you make decisions.<br />Statistics: <br />The science of collecting, organizing, presenting, analyzing and interpreting data to assist in making more effective decisions. <br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Descriptive Statistics: <br />Methods of organizing, summarizing and presenting data in an informative way. <br />Inferential Statistics: <br />Methods used to estimate a property of a population on the basis of a sample. <br />
8. 8. 1. Why Failed in <br />Statistics?<br />Statistics help you make decisions.<br />Descriptive Statistics:<br />Inferential Statistics:<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Population: <br />The entire set of individual or objects of interest or the measurements obtained from all individuals or objects of interest. <br />Sample: <br />A portion, or part, of the population of interest. <br />
9. 9. 1. Why Failed in <br />Statistics?<br />Statistics help you make decisions.<br />Inferential Statistics:<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Population: <br />The entire set of individual or objects of interest or the measurements obtained from all individuals or objects of interest. <br />Sample: <br />A portion, or part, of the population of interest. <br />
10. 10. Types of variables<br />1. Why Failed in <br />Statistics?<br />Qualitative: <br />nonnumeric, attribute<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Quantitative: <br />numerical<br />
11. 11. Types of variables<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Qualitative<br />Quantitative<br />
12. 12. Types of variables<br />1. Why Failed in <br />Statistics?<br />Discrete counting<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />Continuous measuring<br />Discrete<br />Continuous<br />Discrete<br />Continuous<br />Height<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Salary<br />ClassSize<br />
13. 13. Levels of Measurement<br />1. Why Failed in <br />Statistics?<br />Nominal: <br /><ul><li>Data categories are represented by labels or names.
14. 14. Even when the labels are numerically coded, the data categories have no logical order. </li></ul>2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />Ordinal: <br /><ul><li>Data classifications are represented by sets of labels or names (high, medium, low) that have relative values.
15. 15. Because of the relative values, the data classified can be ranked or ordered. </li></ul>3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
16. 16. Levels of Measurement<br />1. Why Failed in <br />Statistics?<br />Nominal: <br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />No logical order<br />Ordinal: <br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Ranked or ordered<br />
17. 17. Levels of Measurement<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />Interval: <br /><ul><li>Similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined.
18. 18. There is no natural zero point. </li></ul>Ratio: <br /><ul><li>The interval level with an inherent zero starting point.
19. 19. Differences and ratios are meaningful for this level of measurement. </li></ul>3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
20. 20. Levels of Measurement<br />1. Why Failed in <br />Statistics?<br />Salary<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />Interval: <br />Ratio: <br />Interval: <br />Ratio: <br />IQ<br />Temperature<br />Distance<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
21. 21. Levels of Measurement<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
22. 22. Levels of Measurement<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
23. 23. Exercises 1-a<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />For each of the following, determinewhether the group is a sample or a population. <br /><ul><li>The participants in a study of a new cholesterol drug.
24. 24. The driverswhoreceived a speeding ticket Kansas City last month.
25. 25. Thoseon welfare in Cook County (Chicago), Illinois.
26. 26. The 30 stocks reported as a part of the Dow Jones Industrial Average. </li></ul>Sample<br />Population<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Population<br />Sample<br />P14. N.4 Ch.1<br />
27. 27. Exercises 1-b<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />Refer to the RealEstate data at the back of the text, which report informationon homes sold in the Denver, Colorado, area last year. Consider the following variables: sellingprice, number of bedrooms, township, and distancefrom the center of the city. <br /><ul><li>Which of the variables are qualitative and which are quantitative?
28. 28. Determin the level of measurementforeach of the variables. </li></ul>3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />township<br />all the rest…<br />Township = nominal level<br />All the rest…=ratio<br />P18. N.16 Ch.1<br />
29. 29. 1. Why Failed in <br />Statistics?<br />Frequency Table: <br /><ul><li>A grouping of qualitative data into mutually exclusive classes showing the number of observations in each class. </li></ul>2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
30. 30. 1. Why Failed in <br />Statistics?<br />Relative Class Frequencies: <br /><ul><li>Show the fraction of the total number of observations in each class</li></ul>2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />RelativeFrequency<br />5/12 = 41.67%<br />3/12=25.00%<br />4/12=33.33%<br />Total 12<br />
31. 31. Exercises 2-a<br />1. Why Failed in <br />Statistics?<br />A total of 1,000 residents in Minnesotawereaskedwhichseasontheypreferred. The resultswere 100 liked winter best, 300 liked spring, 400 likedsummer, and 200 likedfall.<br />If the data weresummarized in a frequencytable, howmany classes wouldbeused? Whatwouldbe the relativefrequenciesforeachclass?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />P27. N.3 .Ch.2<br />
32. 32. GraphicPresentation of Qualitativedata<br />1. Why Failed in <br />Statistics?<br />Bar Chart<br /><ul><li>The classes are reported on the horizontal axis
33. 33. The class frequencies on the vertical axis
34. 34. The class frequencies are proportional to the heights of the bars.</li></ul>2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />RelativeFrequency<br />5/12 = 41.67%<br />3/12=25.00%<br />4/12=33.33%<br />Total 12<br />
35. 35. GraphicPresentation of Qualitativedata<br />1. Why Failed in <br />Statistics?<br />Pie Chart: <br /><ul><li>Shows the proportion or percent that each class represents of the total number of frequencies</li></ul>2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />RelativeFrequency<br />5/12 = 41.67%<br />3/12=25.00%<br />4/12=33.33%<br />Total 12<br />
36. 36. GraphicPresentation of Qualitativedata<br />1. Why Failed in <br />Statistics?<br />Piechartsrequirethatyouinclude all the categoriesthatmake up a whole. Usethemonlywhenyou want to emphasizeeachcategory'srelation to the whole. <br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
37. 37. 1. Why Failed in <br />Statistics?<br />Frequency Distribution: <br /><ul><li>A grouping of data into mutually exclusive classes showing the number of observations in each class.</li></ul>2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
38. 38. 1. Why Failed in <br />Statistics?<br />Frequency Distribution: <br /><ul><li>A grouping of data into mutually exclusive classes showing the number of observations in each class.</li></ul>2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
39. 39. Step 2: Class Interval<br />Step 1: Just enough recipe<br />2 to the k rule<br />10 -< 20 4<br />20 -< 30 1<br />30 -< 40 10<br />40 -< 50 9<br />50 -< 60 3<br />N=27<br />1. Why Failed in <br />Statistics?<br />Frequency Distribution: <br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />N=27 number of class=5<br />22=4 23=8 24=16<br />25=32 26=64 27=128<br /> (55-14)/5 ≈ 8<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Step 3: Choose nice “round” boundaries <br />Step 4: Try to avoid empty and open classes<br />
40. 40. Exercises 2-b<br />><br />\$30 - \$0<br />i = 5<br />1. Why Failed in <br />Statistics?<br />6<br />A set of data consists of 45 observationsbetween \$0 and \$29. Whatsizewouldyourecommendfor the class interval?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />25 = 32, 26 = 64, suggests 6 classes<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Use interval of 5<br />P33. N.8 .Ch.2<br />
41. 41. Exercises 2-b<br />99 - 51<br /> 5<br />1. Why Failed in <br />Statistics?<br />i > ≈ 9<br />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:<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br /> 98 55 62 79 59 51 90 72 56<br />70 62 66 80 94 79 63 73 71 85<br />a. Howmanyclasseswouldyourecommend?<br />a. 24 = 16, 25 = 32, suggests 5 classes<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />b. Whatclass interval wouldyousuggest?<br />b. Use interval of 10<br />P34. N.12.Ch.2<br />
42. 42. Exercises 2-b<br />1. Why Failed in <br />Statistics?<br />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:<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br /> 98 55 62 79 59 51 90 72 56<br />70 62 66 80 94 79 63 73 71 85<br />c. Whatlower limit wouldyourecommendfor the firstclass?<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />c. 50<br />P34. N.12.Ch.2<br />
43. 43. GraphicPresentation of Quantitative data<br />1. Why Failed in <br />Statistics?<br />a) Histogram<br /><ul><li>The classes are marked on the horizontal axis
44. 44. The class frequencies on the vertical axis
45. 45. The class frequencies are represented by the heights of the bars and the bars are adjacent to each other. </li></ul>2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
46. 46. GraphicPresentation of Quantitative data<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />b) Polygon: <br /><ul><li>The shape of a distribution
47. 47. Similar to a histogram</li></ul>3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Not floating in the air <br />
48. 48. GraphicPresentation of Quantitative data<br />1. Why Failed in <br />Statistics?<br />c) Cumulative frequency distribution:<br />used to determine how many or what proportion of the data values are below or above a certain value.<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Notfloating in the air <br />
49. 49. Why Failed in Statistics?<br />1. Why Failed in <br />Statistics?<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
50. 50. GraphicPresentation of Quantitative data<br />1. Why Failed in <br />Statistics?<br />c) Cumulative frequency distribution:<br />used to determine how many or what proportion of the data values are below or above a certain value.<br />2. Chapter 1: What <br />is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: <br />Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />Notfloating in the air <br />
51. 51. Whatwe have learnt?<br />1. Why they failed in Statistics?<br />2. Chapter 1: What is Statistics?<br />Why? What?<br />Types of statistics, variables<br />Levels of measurement<br />3. Chapter 2: Describing Data<br />Frequency tables<br />Frequency distributions<br />Graphic presentation<br />
52. 52. Exercises 1-a<br />Whatis the level of measurement for each of the following variables?<br />A. student IQ ratings <br />B. distance studentstravel to class<br />C. student scores on the first statistics test<br />D. a classification of students by state of birth<br />E. a ranking of students as freshmen, sophomore, junior, and senior<br />F. Number of hoursstudentsstudy per week<br />Interval<br />Ratio<br />Interval<br />Nominal<br />Ordinal<br />Ratio<br />
53. 53. Exercises 1-b<br />Place these variables in the following classification tables. <br />Salary<br />Gender<br />Sales volumen of MP3 players<br />Soft drink preference<br />Temperature<br />SAT scores<br />Student rank in class<br />Rating of a finance professor<br />Number of home computers<br />Discrete<br />Continuous<br />b. Gender<br />d. Soft drink preference<br />Qualitative<br />f. SAT scores<br />a. Salary <br />g. Student rank in class<br />c. Sales volume of MP3 players<br />Quantitative<br />e. Temperature<br />h. Rating of a finance professor<br />i. Number of home computers<br />P16. N.9 Ch.1<br />
54. 54. Exercises 1-c<br />Place these variables in the following classification tables. <br />Salary<br />Gender<br />Sales volumen of MP3 players<br />Soft drink preference<br />Temperature<br />SAT scores<br />Student rank in class<br />Rating of a finance professor<br />Number of home computers<br />Discrete<br />Continuous<br />b. Gender<br />Nominal<br />d. Soft drink preference<br />Ordinal<br />g. Student rank in class<br />h. Rating of a finance professor<br />f. SAT scores<br />e. Temperature<br />Interval<br />a. Salary <br />Ratio<br />c. Sales volume of MP3 players<br />i. Number of home computers<br />
55. 55. Exercises 1-d<br />The tablebelow reports the number of cars and light trucks soldby the Big Three automobile manufacturersforJune 2004 and June 2005. <br />1. Compare the totalsales in the twomonths. What do youconclude? Has there been anincrease in sales?<br />(1,056,144-866,243)<br />866,243<br />Total salesincreased 189,901 units or 21.9%.<br />P17. N.13 Ch.1<br />
56. 56. Exercises 1-d<br />The tablebelow reports the number of cars and light trucks soldby the Big Three automobile manufacturersforJune 2004 and June 2005. <br />2. Compare the percent of the Big Threemarketforeachcompany. Did the marketincreaseordid GM stealsalesfrom the othercompanies? Citeevidence. <br />GM increased the market share by 9 percentage points from 43% to 52%. <br />Crysler lost 3% and Ford lost 6%. <br />All three companies increased the nubmer of units sold. <br />P17. N.13 Ch.1<br />
57. 57. FrequencyDistribution<br />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.<br />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.<br />Step 1: Just enough recipe<br />2 to the k rule<br />Select the smallest number (k) for the number of classes such that 2k is greater than the number of observations (n).<br />
58. 58. FrequencyDistribution<br />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.<br />2 to the k rule<br />Step 1: Just enough recipe<br /><ul><li>If sample size (n) = 1000
59. 59. 21=2; 22=4; 23=8; 24=16; 25=32; 26=64; 27=128; 28=256; 29=512; 210=1024 …
60. 60. The rule suggest 10 classes.
61. 61. If sample size (n) = 80
62. 62. 21=2; 22=4; 23=8; 24=16; 25=32; 26=64; 27=128; …
63. 63. The rule suggest 7 classes.</li></ul>Sample size (n) = 30<br />21=2; 22=4; 23=8; 24=16; 25=32; 26=64; 27=128; …<br />The rule suggest 5 classes.<br />
64. 64. FrequencyDistribution<br />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.<br />Step 2: Class Interval<br /><ul><li>The classes all taken together must cover at least the distance from the lowest value in the raw data to the highest value.
65. 65. The classes must be mutually exclusive and exhaustive.</li></ul>Class interval<br />(next unit of Highest value – lowest value) / number of classes.<br />Usually we will chose some convenient number as class interval that satisfy the inequality.<br />
66. 66. FrequencyDistribution<br />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.<br />Step 2: Class Interval<br /><ul><li>Highest value = 33.9 hours
67. 67. Lowest value = 10.3 hours
68. 68. k=5.
69. 69. Hence, class interval ≥ (33.9-10.3)/5 ≈ 4.7
70. 70. We choose class interval to be 5, some convenient number.</li></li></ul><li>FrequencyDistribution<br />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.<br />Step 3: Individual class limits<br /><ul><li>Next unit of Highest value = 33.9 hours.
71. 71. Lowest value = 10.3 hours.
72. 72. Range = nu of highest – lowest = 23.5.
73. 73. K=5; Interval = 5.
74. 74. With k=5 and interval = 5, the classes will cover a range of 25.
75. 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. 76. 9.55 and 34.55 look odd. Some convenient and close numbers would be 10 and 35.</li></ul>“10 up to 15” means the interval from 10 to 15 that includes 10 but not 15.<br />
77. 77. FrequencyDistribution<br />Step 4: Tally the data<br />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.<br />Example:<br />Hours studying<br />7<br /> 10 up to 15<br />12<br />15 up to 20<br />20 up to 25<br />7<br />25 up to 30<br />3<br />30 up to 35<br />1<br />
78. 78. FrequencyDistribution<br />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.<br />Step 5: Count the number<br />
79. 79. FrequencyDistribution<br />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.<br />Relative Frequency Distribution<br />Step 5: Count the number<br />
80. 80. Exercises 2-b<br />A set of data consists of 38 observations. Howmany classes wouldyourecommendfor the frequency distribution?<br />25 = 32, 26 = 64, therefore, 6 classes<br />A set of data consists of 230 observationsbetween \$235 and \$567. Whatclass interval wouldyourecommend. <br />27 = 128, 28 = 256, suggests 8 classes<br />Classintervals of 40, 45, or 50 all wouldbeacceptable. <br />P33. N.7 .Ch.2<br />
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