2. 1 1 Slide Tuesday August 28 Class 2 Text problems for August 30: Chapter 2 - 2,6 & 10 Aplia Graded Assignment: “Introduction” due September 4, 9:00 am Practice Problems for Chapter 1 & 2 are now available Please note that a tutorial for basic math concepts is available if needed

3. 2 2 Slide n Introduction Statistics: the language

4. 3 3 Slide Data and Data Sets Data are the facts and or numbers collected, summarized, analyzed, and interpreted. Data are the facts and or numbers collected, summarized, analyzed, and interpreted. The data collected in a particular study are referred The data collected in a particular study are referred to as the data set. to as the data set.

5. 4 4 Slide The elements are the entities on which data are The elements are the entities on which data are collected. collected. A variable is a characteristic of interest for the elements. A variable is a characteristic of interest for the elements. The set of measurements collected for a particular The set of measurements collected for a particular element is called an observation. element is called an observation. The total number of data values in a complete data The total number of data values in a complete data set is the number of elements multiplied by the set is the number of elements multiplied by the number of variables. number of variables. Elements, Variables, and Observations

6. 5 5 Slide Stock Annual Earn/ Stock Annual Earn/ Exchange Sales($M) Share($) Data, Data Sets, Elements, Variables, and Observations Company Dataram Dataram EnergySouth EnergySouth Keystone Keystone LandCare LandCare Psychemedics Psychemedics NQ 73.10 0.86 NQ 73.10 0.86 N 74.00 1.67 N 74.00 1.67 N365.70 0.86 N365.70 0.86 NQ111.40 0.33 NQ111.40 0.33 N 17.60 0.13 N 17.60 0.13 Variables Element Names Names Data Set Observation

7. 6 6 Slide Scales of Measurement The scale indicates how the data can be summarized The scale indicates how the data can be summarized and statistical analyses that are most appropriate. The scale indicates how the data can be summarized The scale indicates how the data can be summarized and statistical analyses that are most appropriate. The scale determines the amount of information The scale determines the amount of information contained in the data. contained in the data. The scale determines the amount of information The scale determines the amount of information contained in the data. contained in the data. Scales of measurement include: Scales of measurement include: Nominal Ordinal Interval Ratio

8. 7 7 Slide Scales of Measurement n Nominal A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may be used. Data are labels or names used to identify an Data are labels or names used to identify an attribute of the element. attribute of the element. Data are labels or names used to identify an Data are labels or names used to identify an attribute of the element. attribute of the element.

9. 8 8 Slide Example: Example: Students of a university are classified by the Students of a university are classified by the school in which they are enrolled using a school in which they are enrolled using a nonnumeric label such as Business, Humanities, nonnumeric label such as Business, Humanities, Education, and so on. Education, and so on. Alternatively, a numeric code could be used for Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and 2 denotes Humanities, 3 denotes Education, and so on). so on). Example: Example: Students of a university are classified by the Students of a university are classified by the school in which they are enrolled using a school in which they are enrolled using a nonnumeric label such as Business, Humanities, nonnumeric label such as Business, Humanities, Education, and so on. Education, and so on. Alternatively, a numeric code could be used for Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and 2 denotes Humanities, 3 denotes Education, and so on). so on). Scales of Measurement n Nominal

10. 9 9 Slide Scales of Measurement n Ordinal A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may be used. The data have the properties of nominal data and The data have the properties of nominal data and the order or rank of the data is meaningful. the order or rank of the data is meaningful. The data have the properties of nominal data and The data have the properties of nominal data and the order or rank of the data is meaningful. the order or rank of the data is meaningful.

11. 10 Slide Scales of Measurement n Ordinal Example: Example: Students of a university are classified by their Students of a university are classified by their class standing using a nonnumeric label such as class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior. Freshman, Sophomore, Junior, or Senior. Alternatively, a numeric code could be used for Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on). Freshman, 2 denotes Sophomore, and so on). Example: Example: Students of a university are classified by their Students of a university are classified by their class standing using a nonnumeric label such as class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior. Freshman, Sophomore, Junior, or Senior. Alternatively, a numeric code could be used for Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on). Freshman, 2 denotes Sophomore, and so on).

12. 11 Slide Scales of Measurement n Interval Interval data are always numeric. Interval data are always numeric. The data have the properties of ordinal data, and The data have the properties of ordinal data, and the interval between observations is expressed in the interval between observations is expressed in terms of a fixed unit of measure. terms of a fixed unit of measure. The data have the properties of ordinal data, and The data have the properties of ordinal data, and the interval between observations is expressed in the interval between observations is expressed in terms of a fixed unit of measure. terms of a fixed unit of measure.

13. 12 Slide Scales of Measurement n Interval Example: Example: Melissa has an SAT score of 1205, while Kevin Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 has an SAT score of 1090. Melissa scored 115 points more than Kevin. points more than Kevin. Example: Example: Melissa has an SAT score of 1205, while Kevin Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 has an SAT score of 1090. Melissa scored 115 points more than Kevin. points more than Kevin.

14. 13 Slide Scales of Measurement n Ratio The data have all the properties of interval data The data have all the properties of interval data and the ratio of two values is meaningful. and the ratio of two values is meaningful. The data have all the properties of interval data The data have all the properties of interval data and the ratio of two values is meaningful. and the ratio of two values is meaningful. Variables such as distance, height, weight, and time Variables such as distance, height, weight, and time use the ratio scale. use the ratio scale. Variables such as distance, height, weight, and time Variables such as distance, height, weight, and time use the ratio scale. use the ratio scale. This scale must contain a zero value that indicates This scale must contain a zero value that indicates that nothing exists for the variable at the zero point. that nothing exists for the variable at the zero point. This scale must contain a zero value that indicates This scale must contain a zero value that indicates that nothing exists for the variable at the zero point. that nothing exists for the variable at the zero point.

15. 14 Slide Scales of Measurement n Ratio Example: Example: Melissa’s college record shows 36 credit hours Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned. Kevin has twice as many credit hours earned as Melissa. hours earned as Melissa. Example: Example: Melissa’s college record shows 36 credit hours Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned. Kevin has twice as many credit hours earned as Melissa. hours earned as Melissa.

16. 15 Slide Data can be further classified as being qualitative Data can be further classified as being qualitative or quantitative. or quantitative. Data can be further classified as being qualitative Data can be further classified as being qualitative or quantitative. or quantitative. The statistical analysis that is appropriate depends The statistical analysis that is appropriate depends on whether the data for the variable are qualitative on whether the data for the variable are qualitative or quantitative. or quantitative. The statistical analysis that is appropriate depends The statistical analysis that is appropriate depends on whether the data for the variable are qualitative on whether the data for the variable are qualitative or quantitative. or quantitative. In general, there are more alternatives for statistical In general, there are more alternatives for statistical analysis when the data are quantitative. analysis when the data are quantitative. In general, there are more alternatives for statistical In general, there are more alternatives for statistical analysis when the data are quantitative. analysis when the data are quantitative. Qualitative and Quantitative Data

17. 16 Slide Qualitative Data Labels or names used to identify an attribute of each Labels or names used to identify an attribute of each element element Labels or names used to identify an attribute of each Labels or names used to identify an attribute of each element element Often referred to as categorical data Often referred to as categorical data Use either the nominal or ordinal scale of Use either the nominal or ordinal scale of measurement measurement Use either the nominal or ordinal scale of Use either the nominal or ordinal scale of measurement measurement Can be either numeric or nonnumeric Can be either numeric or nonnumeric

18. 17 Slide Quantitative Data Quantitative data indicate how many or how much: Quantitative data indicate how many or how much: discrete, if measuring how many discrete, if measuring how many continuous, if measuring how much continuous, if measuring how much Quantitative data are always numeric. Quantitative data are always numeric. Ordinary arithmetic operations are meaningful for Ordinary arithmetic operations are meaningful for quantitative data. quantitative data. Ordinary arithmetic operations are meaningful for Ordinary arithmetic operations are meaningful for quantitative data. quantitative data.

19. 18 Slide Scales of Measurement QualitativeQualitative QuantitativeQuantitative NumericalNumerical NumericalNumerical Non-numericalNon-numerical DataData NominalNominalOrdinalOrdinalNominalNominalOrdinalOrdinalIntervalIntervalRatioRatio

20. 19 Slide Cross-Sectional Data Cross-sectional data are collected at the same or Cross-sectional data are collected at the same or approximately the same point in time. approximately the same point in time. Cross-sectional data are collected at the same or Cross-sectional data are collected at the same or approximately the same point in time. approximately the same point in time. Example: data detailing the number of building Example: data detailing the number of building permits issued in June 2007 in each of the counties permits issued in June 2007 in each of the counties of Ohio of Ohio Example: data detailing the number of building Example: data detailing the number of building permits issued in June 2007 in each of the counties permits issued in June 2007 in each of the counties of Ohio of Ohio

21. 20 Slide Time Series Data Time series data are collected over several time Time series data are collected over several time periods. periods. Time series data are collected over several time Time series data are collected over several time periods. periods. Example: data detailing the number of building Example: data detailing the number of building permits issued in Lucas County, Ohio in each of permits issued in Lucas County, Ohio in each of the last 36 months the last 36 months Example: data detailing the number of building Example: data detailing the number of building permits issued in Lucas County, Ohio in each of permits issued in Lucas County, Ohio in each of the last 36 months the last 36 months

22. 21 Slide n Statistical Studies Types of Statistical Studies In experimental studies the variable of interest is first identified. Then one or more other variables are identified and controlled so that data can be obtained about how they influence the variable of interest. In experimental studies the variable of interest is first identified. Then one or more other variables are identified and controlled so that data can be obtained about how they influence the variable of interest. In observational (nonexperimental) studies no In observational (nonexperimental) studies no attempt is made to control or influence the attempt is made to control or influence the variables of interest. variables of interest. In observational (nonexperimental) studies no In observational (nonexperimental) studies no attempt is made to control or influence the attempt is made to control or influence the variables of interest. variables of interest. a survey is a good example

23. 22 Slide Descriptive Statistics n Descriptive statistics are the tabular, graphical, and numerical methods used to summarize and present data.

24. 23 Slide Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide.

25. 24 Slide Example: Hudson Auto Repair Example: Hudson Auto Repair n Sample of Parts Cost ($) for 50 Tune-ups

26. 25 Slide Tabular Summary: Frequency and Percent Frequency Tabular Summary: Frequency and Percent Frequency 50-59 50-59 60-69 60-69 70-79 70-79 80-89 80-89 90-99 90-99 100-109 100-109 2 13 16 7 7 5 50 4 26 32 14 14 10 100 (2/50)100(2/50)100 Parts Cost ($) Cost ($) Parts Frequency Frequency PercentFrequency

27. 26 Slide Graphical Summary: Histogram Graphical Summary: Histogram 2 2 4 4 6 6 8 8 10 12 14 16 18 Parts Cost ($) Parts Cost ($) Frequency 50  59 60  69 70  79 80  89 90  99 100-110 Tune-up Parts Cost

28. 27 Slide Numerical Descriptive Statistics Numerical Descriptive Statistics Hudson’s average cost of parts, based on the 50 Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing the tune-ups studied, is $79 (found by summing the 50 cost values and then dividing by 50). 50 cost values and then dividing by 50). The most common numerical descriptive statistic The most common numerical descriptive statistic is the average (or mean). is the average (or mean).

29. 28 Slide Statistical Inference PopulationPopulation SampleSample Statistical inference CensusCensus Sample survey  the collection of all the elements of interest interest  a subset of the population  the process of using data obtained from a sample to make estimates from a sample to make estimates and test hypotheses about the and test hypotheses about the characteristics of a population characteristics of a population  collecting data for a population  collecting data for a sample

30. 29 Slide Process of Statistical Inference Process of Statistical Inference 1. Population 1. Population consists of all tune- ups. Average cost of parts is unknown parts is unknown. 1. Population 1. Population consists of all tune- ups. Average cost of parts is unknown parts is unknown. 2. A sample of 50 2. A sample of 50 engine tune-ups is examined. 2. A sample of 50 2. A sample of 50 engine tune-ups is examined. 3.The sample data provide a sample average parts cost of $79 per tune-up. 3.The sample data provide a sample average parts cost of $79 per tune-up. 4. The sample average 4. The sample average is used to estimate the population average. 4. The sample average 4. The sample average is used to estimate the population average.

31. 30 Slide Computers and Statistical Analysis Statistical analysis typically involves working with Statistical analysis typically involves working with large amounts of data. large amounts of data. Computer software is typically used to conduct the Computer software is typically used to conduct the analysis. analysis. Instructions are provided in chapter appendices for Instructions are provided in chapter appendices for carrying out many of the statistical procedures carrying out many of the statistical procedures using Minitab and Excel. using Minitab and Excel.

32. 31 Slide Tainted Truth n “ If someone is misusing numbers and scaring us with those numbers to get us to do something, however good that something is, we have lost the power of numbers” n WE ALL NEED TO BE CRITICAL.

33. 32 Slide Reported Information n Eating oat brand is a cheap and easy way to reduce your cholesterol count (Quaker Oats) Actual Study Information n Diet must consist of nothing but oat bran to achieve a slightly lower cholesterol count.

34. 33 Slide Reported Information n Only 29% of high school girls are happy with themselves, compared to 66% of elementary school girls. (American Association of University Women) Actual Study Information n Of 3000 high school girls 29% responded “Always true” to the statement, “I am happy with the way I am.” Most answered, “Sort of true” and “Sometimes true.”

35. 34 Slide ?????? Credible n Four out of five people in Columbia prefer Wendys over McDonalds (according to a recent survey)

36. 35 Slide

37. 36 Slide

38. 37 Slide n Ethical Guidelines for Statistical Practice American Statistical Association www.amstat.org

39. 38 Slide n Association vs Causation

40. 39 Slide Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations n Summarizing Qualitative Data n Summarizing Quantitative Data

41. 40 Slide Summarizing Qualitative Data n Frequency Distribution n Relative Frequency Distribution n Percent Frequency Distribution n Bar Graphs n Pie Charts

42. 41 Slide A frequency distribution is a tabular summary of A frequency distribution is a tabular summary of data showing the frequency (or number) of items data showing the frequency (or number) of items in each of several non-overlapping classes. in each of several non-overlapping classes. A frequency distribution is a tabular summary of A frequency distribution is a tabular summary of data showing the frequency (or number) of items data showing the frequency (or number) of items in each of several non-overlapping classes. in each of several non-overlapping classes. The objective is to provide insights about the data The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data. The objective is to provide insights about the data The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data. Frequency Distribution

43. 42 Slide Example: Marada Inn Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are: Below Average Below Average Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Below Average Below Average Poor Poor Excellent Excellent Above Average Above Average Average Average Above Average Above Average Below Average Below Average Poor Poor Above Average Above Average Average Average

44. 43 Slide Frequency Distribution Poor Below Average Average Above Average Excellent 2 3 5 9 1 Total 20 RatingFrequency

45. 44 Slide The relative frequency of a class is the fraction or The relative frequency of a class is the fraction or proportion of the total number of data items proportion of the total number of data items belonging to the class. belonging to the class. The relative frequency of a class is the fraction or The relative frequency of a class is the fraction or proportion of the total number of data items proportion of the total number of data items belonging to the class. belonging to the class. A relative frequency distribution is a tabular A relative frequency distribution is a tabular summary of a set of data showing the relative summary of a set of data showing the relative frequency for each class. frequency for each class. A relative frequency distribution is a tabular A relative frequency distribution is a tabular summary of a set of data showing the relative summary of a set of data showing the relative frequency for each class. frequency for each class. Relative Frequency Distribution

46. 45 Slide Percent Frequency Distribution The percent frequency of a class is the relative The percent frequency of a class is the relative frequency multiplied by 100. frequency multiplied by 100. The percent frequency of a class is the relative The percent frequency of a class is the relative frequency multiplied by 100. frequency multiplied by 100. A percent frequency distribution is a tabular A percent frequency distribution is a tabular summary of a set of data showing the percent summary of a set of data showing the percent frequency for each class. frequency for each class. A percent frequency distribution is a tabular A percent frequency distribution is a tabular summary of a set of data showing the percent summary of a set of data showing the percent frequency for each class. frequency for each class.

47. 46 Slide Relative Frequency and Percent Frequency Distributions Poor Below Average Average Above Average Excellent.10.15.25.45.05 Total 1.00 10 15 25 45 5 100 Relative RelativeFrequency Percent PercentFrequency Rating.10(100) = 10 1/20 =.05

48. 47 Slide Bar Graph A bar graph is a graphical device for depicting A bar graph is a graphical device for depicting qualitative data. qualitative data. On one axis (usually the horizontal axis), we specify On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes. the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the scale can be used for the other axis (usually the vertical axis). vertical axis). Using a bar of fixed width drawn above each class Using a bar of fixed width drawn above each class label, we extend the height appropriately. label, we extend the height appropriately. The bars are separated to emphasize the fact that each The bars are separated to emphasize the fact that each class is a separate category. class is a separate category.

49. 48 Slide Poor Below Average Below Average Above Average Above Average Excellent Frequency Rating Bar Graph 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 Marada Inn Quality Ratings

50. 49 Slide Pie Chart The pie chart is another commonly used graphical device The pie chart is another commonly used graphical device for presenting relative frequency distributions for for presenting relative frequency distributions for qualitative data. qualitative data. n First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to subdivide the circle into sectors that correspond to the relative frequency for each class. to the relative frequency for each class. n Since there are 360 degrees in a circle, a class with a relative frequency of.25 would consume.25(360) = 90 relative frequency of.25 would consume.25(360) = 90 degrees of the circle. degrees of the circle.

51. 50 Slide Below Average 15% Below Average 15% Average 25% Average 25% Above Average 45% Above Average 45% Poor 10% Poor 10% Excellent 5% Excellent 5% Marada InnQuality Ratings Marada Inn Quality Ratings Pie Chart

52. 51 Slide n Insights Gained from the Preceding Pie Chart Example: Marada Inn One-half of the customers surveyed gave Marada One-half of the customers surveyed gave Marada a quality rating of “above average” or “excellent” a quality rating of “above average” or “excellent” (looking at the left side of the pie). This might (looking at the left side of the pie). This might please the manager. please the manager. For each customer who gave an “excellent” rating, For each customer who gave an “excellent” rating, there were two customers who gave a “poor” there were two customers who gave a “poor” rating (looking at the top of the pie). This should rating (looking at the top of the pie). This should displease the manager. displease the manager.

53. 52 Slide Below Average 15% Below Average 15% Average 25% Average 25% Above Average 45% Above Average 45% Poor 10% Poor 10% Excellent 5% Excellent 5% Marada InnQuality Ratings Marada Inn Quality Ratings Pie Chart

54. 53 Slide See Example 1 Class 2 data file Text problems for August 30: Chapter 2 – 2, 6 & 10

55. 54 Slide

56. 55 Slide