1 1 slide © 2002 south-western /thomson learning

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© 2002 South-Western /Thomson Learning© 2002 South-Western /Thomson Learning

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Chapter 1 Data and Statistics

Applications in Business and Economics Data Data Sources Descriptive Statistics Statistical Inference

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Applications in Business and Economics

AccountingPublic 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.

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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

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Data IN

Elements, Variables, and Observations Scales of Measurement Qualitative and Quantitative Data Cross-Sectional and Time Series Data

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Data and Data Sets

Data 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.

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Elements, Variables, and Observations IN

The 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.

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Data, Data Sets, Elements, Variables, and

Observations IN

ElementElementss

VariableVariabless

Data SetData Set DatumDatum

ObservatioObservationn

StockStock Annual Annual Earn/Earn/

CompanyCompany Exchange Sales($M) Sh. Exchange Sales($M) Sh.($)($)

DataramDataram AMEXAMEX 73.1073.10 0.86 0.86

EnergySouthEnergySouth OTC OTC 74.0074.00 1.67 1.67

KeystoneKeystone NYSE NYSE 365.70 365.70 0.86 0.86

LandCareLandCare NYSE NYSE 111.40 111.40 0.330.33

PsychemedicsPsychemedics AMEXAMEX 17.6017.60 0.13 0.13

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Scales of Measurement IN

Scales of measurement include:• Nominal• Ordinal• Interval• Ratio

The scale determines the amount of information contained in the data.

The scale indicates the data summarization and statistical analyses that are most appropriate.

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Nominal• Data are labels or names used to identify an

attribute of the element.• A nonnumeric label or a numeric code may

be used.

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Nominal• Example:

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).

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Ordinal• The 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.

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Ordinal• Example:

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).

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Interval• The 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.

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Interval• Example:

Melissa has an SAT score of 1205, while Kevin has an SAT score of 1090. Melissa scored 115 points more than Kevin.

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Ratio• The 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.

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Ratio• Example:

Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned as Melissa.

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Qualitative and Quantitative Data IN

Data 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.

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Qualitative Data IN

Qualitative 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.

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Quantitative Data IN

Quantitative 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.

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Cross-Sectional and Time Series Data

Cross-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 Texas

Time 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

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Data Sources

Existing Sources• Data 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.

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Data Sources

Existing Sources• Government agencies are another

important source of data.• Data are also available from a variety of

industry associations and special-interest organizations.

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Data Sources

Internet• The 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.

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Statistical Studies• Statistical 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

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Data Acquisition Considerations

Time Requirement• Searching for information can be time

consuming.• Information might no longer be useful by the

time it is available. Cost of Acquisition

• Organizations often charge for information even when it is not their primary business activity.

Data Errors• Using any data that happens to be available or

that were acquired with little care can lead to poor and misleading information.

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Descriptive Statistics

Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.

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91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

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 below.

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Tabular Summary (Frequencies and Percent Frequencies)

Parts Percent Cost ($) Frequency

Frequency 50-59 2 4 60-69 13 26 70-79 16 32 80-89 7 14 90-99 7 14 100-109 5 10

Total 50 100

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Graphical Summary (Histogram)

PartsCost ($)PartsCost ($)

22

44

66

88

1010

1212

1414

1616

1818

Fre

qu

en

cy

Fre

qu

en

cy

50 60 70 80 90 100 11050 60 70 80 90 100 110

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Numerical Descriptive Statistics• The most common numerical descriptive

statistic is the average (or mean). • Hudson’s 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).

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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).

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Process of Statistical Inference

1. Population 1. Population consists of allconsists of all

tune-ups. Averagetune-ups. Averagecost of parts iscost of parts is

unknownunknown.

2. A sample of 502. A sample of 50engine tune-ups engine tune-ups

is examined.is examined.

3. The sample data 3. The sample data provide a sampleprovide a sampleaverage cost ofaverage cost of

$79 per tune-up$79 per tune-up..

4. The value of the 4. The value of the sample average is usedsample average is usedto make an estimate ofto make an estimate of the population average.the population average.

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