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1 1 Slide © 2006 Thomson/South-Western Chapter 1 Data and Statistics I need help! Applications in Business and Economics Data Data Sources Descriptive Statistics Statistical Inference Computers and Statistical Analysis

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2 2 Slide © 2006 Thomson/South-Western Data and Data Sets n Data are the facts and figures collected, summarized, analyzed, and interpreted. The data collected in a particular study are The data collected in a particular study are referred to as the data set. referred to as the data set.

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3 3 Slide © 2006 Thomson/South-Western 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 the elements. A variable is a characteristic of 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. Elements, Variables, and Observations

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4 4 Slide © 2006 Thomson/South-Western 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 AMEX 73.10 0.86 AMEX 73.10 0.86 OTC 74.00 1.67 OTC 74.00 1.67 NYSE365.70 0.86 NYSE365.70 0.86 NYSE111.40 0.33 NYSE111.40 0.33 AMEX 17.60 0.13 AMEX 17.60 0.13 Variables Element Names Names Data Set Observation

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5 5 Slide © 2006 Thomson/South-Western Scales of Measurement The scale indicates the data summarization and The scale indicates the data summarization and statistical analyses that are most appropriate. statistical analyses that are most appropriate. The scale indicates the data summarization and The scale indicates the data summarization and statistical analyses that are most appropriate. 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

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6 6 Slide © 2006 Thomson/South-Western Scales of Measurement n Nominal = name categories, count frequencies A nonnumeric label or numeric code may A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may 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.

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7 7 Slide © 2006 Thomson/South-Western 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. 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. Scales of Measurement n Nominal

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8 8 Slide © 2006 Thomson/South-Western Scales of Measurement n Ordinal = rank categories in order, but no meaningful distance A nonnumeric label or numeric code may A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may A nonnumeric label or numeric code may be used. The data have the properties of nominal data The data have the properties of nominal data And order or rank of the data is meaningful. The data have the properties of nominal data The data have the properties of nominal data And order or rank of the data is meaningful.

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9 9 Slide © 2006 Thomson/South-Western 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. 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.

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10 Slide © 2006 Thomson/South-Western Scales of Measurement n Interval = equal distance between scores; numerical Interval data are always numeric. Interval data are always numeric. The data have the properties of ordinal data, The data have the properties of ordinal data, and the interval between observations is and the interval between observations is a fixed unit of measure. The data have the properties of ordinal data, The data have the properties of ordinal data, and the interval between observations is and the interval between observations is a fixed unit of measure.

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11 Slide © 2006 Thomson/South-Western 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.

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12 Slide © 2006 Thomson/South-Western Scales of Measurement n Ratio = equal distance, meaningful zero The data have all the properties of interval The data have all the properties of interval data and the ratio of two values is meaningful. The data have all the properties of interval The data have all the properties of interval data and the ratio of two values is meaningful. Distance, height, weight, and time use the ratio scale. use the ratio scale. Distance, height, weight, and time use the ratio scale. use the ratio scale. This scale must contain a zero value for This scale must contain a zero value for which nothing exists for the variable This scale must contain a zero value for This scale must contain a zero value for which nothing exists for the variable

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13 Slide © 2006 Thomson/South-Western 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.

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14 Slide © 2006 Thomson/South-Western 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 Appropriate statistical analyses are rather limited Appropriate statistical analyses are rather limited

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15 Slide © 2006 Thomson/South-Western 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.

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16 Slide © 2006 Thomson/South-Western Scales of Measurement QualitativeQualitativeQuantitativeQuantitative NumericalNumerical NumericalNumerical NonnumericalNonnumerical DataData NominalNominalOrdinalOrdinalNominalNominalOrdinalOrdinalIntervalIntervalRatioRatio

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17 Slide © 2006 Thomson/South-Western Descriptive Statistics n Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.

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18 Slide © 2006 Thomson/South-Western 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.

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19 Slide © 2006 Thomson/South-Western Example: Hudson Auto Repair Example: Hudson Auto Repair n Sample of Parts Cost for 50 Tune-ups

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20 Slide © 2006 Thomson/South-Western 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 13 16 16 7 7 5 5 50 50 4 26 26 32 32 14 14 10 10 100 100 (2/50)100 Parts Cost ($) Cost ($) Parts Frequency Frequency PercentFrequency

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21 Slide © 2006 Thomson/South-Western 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

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22 Slide © 2006 Thomson/South-Western Inferential Statistics n Uses samples from larger populations n Draw conclusions from sample data n Conclusions apply to whole population n Estimate a population value n Test a hypothesis n State probability of error

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