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A term too broad to define, Statistics is an important subject studied by almost all commerce graduates and undergraduates across the globe.

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

Application Areas of Statistics

Accounting– Auditing– Costing

Statistics– Financial trends– Forecasting

Management– Describe employees– Quality improvement

Marketing– Consumer preferences– Marketing mix effects

Applications in Business and Economics

• Accounting

Economics

Public accounting firms use statisticalsampling procedures when conductingaudits for their clients.

Economists use statistical informationin making forecasts about the future ofthe economy or some aspect of it.

A variety of statistical quality control charts are used to monitorthe output of a production process.

Production

Electronic point-of-sale scanners atretail checkout counters are used tocollect data for a variety of marketingresearch applications.

Marketing

Financial advisors use price-earnings ratios anddividend yields to guide their investmentrecommendations.

Statistics

Why Collect Data?

Obtain input to a research studyMeasure performanceAssist in formulating decision alternativesSatisfy curiosity

– Knowledge for the sake of knowledge

Data and Data Sets

• Data are the facts and figures collected, summarized, analyzed, and interpreted.

The data collected in a particular study are referred to as the data set.

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.

Elements, Variables, and Observations

Stock Annual Earn/Exchange Sales($M) Share($)

Data, Data Sets, Elements, Variables, and Observations

Company

Dataram EnergySouth Keystone LandCare Psychemedics

AMEX 73.10 0.86 OTC 74.00 1.67 NYSE 365.70 0.86 NYSE 111.40 0.33 AMEX 17.60 0.13

VariablesElement Names

Data Set

Observation

Scales of Measurement

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

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

Scales of measurement include:Nominal

Ordinal

Interval

Scales of Measurement• Nominal

A nonnumeric label or numeric code may be used.

Data are labels or names used to identify an attribute of the element.

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).

Scales of Measurement Nominal

Scales of Measurement• Ordinal

A nonnumeric label or numeric code may be used.

The data have the properties of nominal data and the order or rank of the data is meaningful.

Scales of Measurement• 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).

Interval data are always numeric.

The data have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure.

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

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.

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.

Types of DataData

Numerical(Quantitative)

Categorical(Qualitative)

Discrete Continuous

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.

Qualitative and Quantitative Data

Qualitative Data Labels or names used to identify an attribute of each element

Often referred to as categorical data

Use either the nominal or ordinal scale of measurement

Can be either numeric or nonnumeric

Appropriate statistical analyses are rather limited

Quantitative Data

Quantitative data indicate how many or how much: discrete, if measuring how many

continuous, if measuring how much

Quantitative data are always numeric.

Ordinary arithmetic operations are meaningful for quantitative data.

Qualitative Quantitative

Numerical NumericalNon-numerical

Nominal

Ordinal

Nominal Ordinal Interval Ratio

Cross-Sectional 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 2003 in each of the counties of Ohio

Time Series Data

Time series data are collected over several time periods.

Example: data detailing the number of building permits issued in Lucas County, Ohio in each of the last 36 months

DataSources

Primary Secondary

Experiment Published(& On-Line)

Survey Observation

Data Sources

Data Sources• Existing Sources

Within a firm – almost any departmentBusiness database services – Dow Jones & Co.Government agencies - U.S. Department of LaborIndustry associations – Travel Industry Association of AmericaSpecial-interest organizations – Graduate Management Admission CouncilInternet – more and more firms

• Statistical Studies

Data Sources (Continued)

In experimental studies the variables of interestare first identified. Then one or more factors arecontrolled so that data can be obtained about howthe factors influence the variables.

In observational (non-experimental) studies no attempt is made to control or influence the variables of interest. a survey is a

good example

Data Acquisition Considerations

Time Requirement

Cost of Acquisition

Data Errors

• Searching for information can be time consuming.• Information may no longer be useful by the time it

is available.

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

• Using any data that happens to be available or that were acquired with little care can lead to poor and misleading information.

What Is Statistics?

• Collecting data– e.g., Survey

• Presenting data– e.g., Charts & tables

• Characterizing data– e.g., Average

Data Analysis

Decision-Making

Statistical MethodsStatisticalMethods

DescriptiveStatistics

InferentialStatistics

Descriptive Statistics

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

Descriptive Statistics: These are statistical methods used to describe data that have been collected.

Example: Hudson Auto Repair

The manager of Hudson Autowould like to have a betterunderstanding of the costof parts used in the enginetune-ups performed in theshop. She examines 50customer invoices for tune-ups. The costs of

parts,rounded to the nearest dollar, are listed on the

nextslide.

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

Tabular Summary: Frequency and Percent Frequency

50-59 60-69 70-79 80-89 90-99 100-109

2 13 16 7 7 5 50

4 26 32 14 14 10 100

(2/50)100

Parts Cost ($)

Parts Frequency

PercentFrequency

Graphical Summary: Histogram

1012141618

PartsCost ($)

50-59 60-69 70-79 80-89 90-99 100-110

Tune-up Parts Cost

Numerical Descriptive Statistics

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).

The most common numerical descriptive statistic is the average (or mean).

Inferential Statistics• Involves

– Estimation– Hypothesis

testing

• Purpose– Make decisions about

population characteristics

Population?

Inferential Statistics: These are statistical methods used to find out something about population based on a sample.

Statistical Inference

Population

Sample

Statistical inference

Census

Sample survey

- the set of all elements of interest in a particular study

- a subset of the population

- the process of using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population

- collecting data for a population

- collecting data for a sample

Process 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 parts costof $79 per tune-up.

4. The sample averageis used to estimate the population average.

Statistical Analysis Using Microsoft Excel

Computer software is typically used to conduct the analysis. Frequently the data that is to be analyzed resides in a spreadsheet. Modern spreadsheet packages are capable of data management, analysis, and presentation. MS Excel is the most widely available spreadsheet software in business organizations.

Statistical Analysis Using Microsoft Excel 3 tasks might be

needed:• Enter Data• Enter Functions and Formulas• Apply Tools

1Parts Cost

2 913 714 1045 856 627 788 69

D EMean =AVERAGE(A2:A71)

Median =MEDIAN(A2:A71)Mode =MODE(A2:A71)

Range =MAX(A2:A71)-MIN(A2:A71)

Excel Worksheet (showing data)

Note: Rows 10-51 are not shown.

A B C D

1 Customer Invoice #Parts

Cost ($)Labor

Cost ($)2 Sam Abrams 20994 91 1853 Mary Gagnon 21003 71 2054 Ted Dunn 21010 104 1925 ABC Appliances 21094 85 1786 Harry Morgan 21116 62 2427 Sara Morehead 21155 78 1488 Vista Travel, Inc. 21172 69 1659 John Williams 21198 74 190

Excel Formula Worksheet

Note: Columns A-B and rows 10-51 are not shown.

C D E F G

1Parts

Cost ($)Labor

Cost ($)2 91 185 Average Parts Cost =AVERAGE(C2:C51)3 71 2054 104 1925 85 1786 62 2427 78 1488 69 1659 74 190

Excel Value Worksheet

Note: Columns A-B and rows 10-51 are not shown.

C D E F G

1Parts

Cost ($)Labor

Cost ($)2 91 185 Average Parts Cost 793 71 2054 104 1925 85 1786 62 2427 78 1488 69 1659 74 190

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