DATA AND STATISTICS
Slides Prepared byJOHN S. LOUCKSSt. Edwards University 2002 South-Western /Thomson LearningTM
# Slide#Chapter 1 Data and StatisticsApplications in Business and EconomicsDataData SourcesDescriptive StatisticsStatistical Inference # Slide#Applications in Business and EconomicsAccountingPublic accounting firms use statistical sampling procedures when conducting audits for their clients.FinanceFinancial advisors use a variety of statistical information, including price-earnings ratios and dividend yields, to guide their investment recommendations.MarketingElectronic point-of-sale scanners at retail checkout counters are being used to collect data for a variety of marketing research applications. # Slide#ProductionA variety of statistical quality control charts are used to monitor the output of a production process.EconomicsEconomists use statistical information in making forecasts about the future of the economy or some aspect of it.Applications in Business and Economics # Slide#DataElements, Variables, and ObservationsScales of MeasurementQualitative and Quantitative DataCross-Sectional and Time Series Data # Slide#Data and Data SetsData are the facts and figures that are collected, summarized, analyzed, and interpreted.The data collected in a particular study are referred to as the data set. # Slide#Elements, Variables, and ObservationsThe elements are the entities on which data are collected.A variable is a characteristic of interest for the elements.The set of measurements collected for a particular element is called an observation.The total number of data values in a data set is the number of elements multiplied by the number of variables.
# Slide#Data, Data Sets, Elements, Variables, and ObservationsElementsVariablesData SetDatumObservation Stock Annual Earn/Company Exchange Sales($M) Sh.($)
DataramAMEX73.10 0.86EnergySouth OTC74.00 1.67Keystone NYSE 365.70 0.86 LandCare NYSE 111.40 0.33PsychemedicsAMEX17.60 0.13 # Slide#Scales of MeasurementScales of measurement include:NominalOrdinalIntervalRatioThe scale determines the amount of information contained in the data.The scale indicates the data summarization and statistical analyses that are most appropriate. # Slide#Scales of MeasurementNominalData are labels or names used to identify an attribute of the element.A nonnumeric label or a numeric code may be used. # Slide#Scales of MeasurementNominalExample: Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on.
Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and so on).
# Slide#Scales of MeasurementOrdinalThe data have the properties of nominal data and the order or rank of the data is meaningful.A nonnumeric label or a numeric code may be used.
# Slide#Scales of MeasurementOrdinalExample: Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior.
Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on). # Slide#Scales of MeasurementIntervalThe data have the properties of ordinal data and the interval between observations is expressed in terms of a fixed unit of measure.Interval data are always numeric.
# Slide#Scales of MeasurementIntervalExample: Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 points more than Kevin.
# Slide#Scales of MeasurementRatioThe data have all the properties of interval data and the ratio of two values is meaningful.Variables such as distance, height, weight, and time use the ratio scale.This scale must contain a zero value that indicates that nothing exists for the variable at the zero point. # Slide#Scales of MeasurementRatioExample: Melissas college record shows 36 credit hours earned, while Kevins record shows 72 credit hours earned. Kevin has twice as many credit hours earned as Melissa.
# Slide#Qualitative and Quantitative DataData can be further classified as being qualitative or quantitative.The statistical analysis that is appropriate depends on whether the data for the variable are qualitative or quantitative.In general, there are more alternatives for statistical analysis when the data are quantitative. # Slide#Qualitative DataQualitative data are labels or names used to identify an attribute of each element.Qualitative data use either the nominal or ordinal scale of measurement.Qualitative data can be either numeric or nonnumeric.The statistical analysis for qualitative data are rather limited. # Slide#Quantitative DataQuantitative data indicate either how many or how much.Quantitative data that measure how many are discrete.Quantitative data that measure how much are continuous because there is no separation between the possible values for the data..Quantitative data are always numeric.Ordinary arithmetic operations are meaningful only with quantitative data.
# Slide#Cross-Sectional and Time Series DataCross-sectional data are collected at the same or approximately the same point in time.Example: data detailing the number of building permits issued in June 2000 in each of the counties of TexasTime series data are collected over several time periods.Example: data detailing the number of building permits issued in Travis County, Texas in each of the last 36 months # Slide#Data SourcesExisting SourcesData needed for a particular application might already exist within a firm. Detailed information is often kept on customers, suppliers, and employees for example.Substantial amounts of business and economic data are available from organizations that specialize in collecting and maintaining data. # Slide#Data SourcesExisting SourcesGovernment agencies are another important source of data.Data are also available from a variety of industry associations and special-interest organizations.
# Slide#Data SourcesInternetThe Internet has become an important source of data.Most government agencies, like the Bureau of the Census (www.census.gov), make their data available through a web site.More and more companies are creating web sites and providing public access to them.A number of companies now specialize in making information available over the Internet. # Slide#Statistical StudiesStatistical studies can be classified as either experimental or observational.In experimental studies the variables of interest are first identified. Then one or more factors are controlled so that data can be obtained about how the factors influence the variables.In observational (nonexperimental) studies no attempt is made to control or influence the variables of interest.A survey is perhaps the most common type of observational study.Data Sources # Slide#Data Acquisition ConsiderationsTime RequirementSearching for information can be time consuming.Information might no longer be useful by the time it is available.Cost of AcquisitionOrganizations often charge for information even when it is not their primary business activity.Data ErrorsUsing any data that happens to be available or that were acquired with little care can lead to poor and misleading information. # Slide#Descriptive StatisticsDescriptive statistics are the tabular, graphical, and numerical methods used to summarize data. # Slide#
Example: Hudson Auto RepairThe manager of Hudson Auto would like to havea better understanding of the cost of parts used in theengine tune-ups performed in the shop. She examines50 customer invoices for tune-ups. The costs of parts,rounded to the nearest dollar, are listed below.
# Slide#Example: Hudson Auto RepairTabular Summary (Frequencies and Percent Frequencies)
Parts Percent Cost ($) Frequency Frequency 50-59 2 4 60-69 1326 70-791632 80-89 714 90-99 714 100-109 510 Total 50 100
# Slide#Example: Hudson Auto RepairGraphical Summary (Histogram)PartsCost ($)24681012141618Frequency50 60 70 80 90 100 110 # Slide#Example: Hudson Auto RepairNumerical Descriptive StatisticsThe most common numerical descriptive statistic is the average (or mean). Hudsons average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing the 50 cost values and then dividing by 50).
# Slide#Statistical Inference Statistical inference is the process of using data obtained from a small group of elements (the sample) to make estimates and test hypotheses about the characteristics of a larger group of elements (the population). # Slide#Example: Hudson Auto RepairProcess of Statistical Inference1. Population consists of alltune-ups. Averagecost of parts isunknown.2. A sample of 50engine tune-ups is examined.3. The sample data provide a sampleaverage cost of$79 per tune-up.4. The value of the sample average is usedto make an estimate of the population average. # Slide#End of Chapter 1 # Slide#Sheet191789357755299809762716972896675797572761047462689710577658010985978868836871696774628298101791057969627378.98