Data and Statistics

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Chapter 1STATISTICS in PRACTICE

• BUSINESS WEEK
• Most issues of Business Week provide an in-depth
  report on a topic of current interest. Often, the
  in-depth reports contain statistical facts and
  summaries that help the reader understand the
  business and economic information.
• Business Week also uses statistics and
  statistical information in managing its own
  business.

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Chapter 1Data and Statistics

• 1.1 Applications in Business and Economics
• 1.2 Data
• 1.3 Data Sources
• 1.4 Descriptive Statistics
• 1.5 Statistical Inference
• 1.6 Computers and Statistical Analysis

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1.1 Applications in Business and Economics

• Accounting
• Finance
• Marketing
• Production
• Economics

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Applications in Business and Economics

• Accounting
• Public accounting firms use statistical
• sampling procedures when conducting audits
  for
• their clients.
• For instance, the audit staff selects a subset of
  the accounts
• called a sample. After reviewing the accuracy
  of the
• sampled accounts, the auditors draw a
  conclusion as to
• whether the accounts receivable amount shown
  on the
• clients balance sheet is acceptable.

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Applications in Business and Economics

• Economics
• Economists use statistical information in
  making forecasts
• about the future of the economy or some
  aspect of it.
• For instance, the analysts review a
• variety of financial data including
• price/earnings ratios and dividend
• yields. By comparing the information
• for an individual stock with information
• about the stock market averages, a financial
  analyst
• can begin to draw a conclusion as to whether
  an individual
• stock is over- or under priced.

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Applications in Business and Economics

• Marketing
• Electronic point-of-sale scanners at retail
  checkout counters
• are used to collect data for a variety of
  marketing
• research applications.
• For example, Brand managers can review the
• Scanner statistics and the promotional activity
  
• statistics to gain a better understanding of
  the
• Relationship between promotional activities and
  sales.
• Such analyses often prove helpful in
  establishing future
• marketing strategies for the various products.

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Applications in Business and Economics

• Production
• A variety of statistical quality control
• charts are used to monitor the output
• of a production process.
• For example, that a machine fills containers with
  
• 12 ounces of a soft drink. Periodically, a
  production
• worker selects a sample of containers and
  computes
• the average number of ounces in the sample.
  Properly
• interpret the average can help determine when
  
• adjustments are necessary to correct a
  production
• process.

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Applications in Business and Economics

• Finance
• Financial advisors use price-earnings ratios
  and dividend
• yields to guide their investment
  recommendations.

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1.2 Data

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

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1.2 Data

• 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.

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Elements, Variables, and Observations

• 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

• the data set contains 8 elements.
• five variables Exchange, Ticker Symbol, Market
  Cap,
• Price/Earnings Ratio,
  Gross Profit Margin.
• observations the first observation (DeWolfe
  Companies)
• is AMEX, DWL, 36.4, 8.4, and 36.7.

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Data, Data Sets, Elements, Variables, and
Observations
Stock Annual Earn/ Exchange
Sales(M) Share()
Company
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
Dataram EnergySouth Keystone LandCare
Psychemedics
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Scales of Measurement

• Nominal scale
• When the data for a variable consist of
  labels or names used to identify an attribute of
  the element.
• For example, gender, ID number,
  exchange variable
  in Table 1.1
• nominal data can be recorded using a
  numeric code. We could use 0 for female, and
  1 for male.

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Scales of Measurement

• 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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Scales of Measurement

• Ordinal scale
• if the data exhibit the properties of nominal
  data and the order or rank of the data is
  meaningful.
• For example, questionnaire a repair service
  rating of excellent, good, or poor.
• Ordinal data can be recorded using a numeric
  code. We could use 1 for excellent, 2 for good,
  and 3 for poor.

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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).

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Scales of Measurement

• Interval
• the data show the properties of ordinal data
  and the interval between values is expressed in
  terms of a fixed unit of measure.
• Example SAT scores, temperature.
• Interval data are always numeric.

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Scales of Measurement

• Interval
• Example
• three students with SAT scores of 1120, 1050,
  and 970 can be ranked or ordered in terms of
  best performance to poorest performance.
• In addition, the differences between the
  scores are meaningful. For instance, student 1
  scored 1120 1050 70 points more than student
  2, while student 2 scored 1050 970 80 points
  more than student 3.

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Scales of Measurement

• Ratio
• the data have all the properties of interval
  data and the ratio of two values is meaningful.
• Ratio scale requires that a zero value be
  included to indicate that nothing exists for the
  variable at the zero point.
• For example, distance, height, weight, and time
  use the ratio scale of measurement.

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Scales of Measurement

• Ratio
• Example
• 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.

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Qualitative and Quantitative Data

• Data can be further classified as either
  qualitative or quantitative.
• The statistical analysis appropriate for a
  particular variable depends upon whether the
  variable is qualitative or quantitative.
• If the variable is qualitative, the statistical
  analysis is rather limited.
• In general, there are more alternatives for
  statistical analysis when the data are
  quantitative.

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Qualitative Data

• Labels or names used to identify an attribute of
  each element
• Qualitative data are 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

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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.

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Scales of Measurement
Data
Qualitative
Quantitative
Numerical
Numerical
Nonnumerical
Nominal
Ordinal
Nominal
Ordinal
Interval
Ratio
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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
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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
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Data Sources

• Existing Sources

Within a firm almost any department
Business database services Dow Jones Co.
Government agencies - U.S. Department of Labor
Industry associations Travel Industry
Association
of America
Special-interest organizations Graduate
Management
Admission Council
Internet more and more firms
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1.3 Data Sources

• Existing Sources
• Statistical Studies
• Data Acquisition Errors

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Data Sources

• Statistical Studies

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.
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Data Acquisition Considerations
Time Requirement

• Searching for information can be time
  consuming.

• Information may 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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1.4 Descriptive Statistics

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

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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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Example Hudson Auto Repair

• Sample of Parts Cost for 50 Tune-ups

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Tabular Summary Frequency and Percent
Frequency
Parts Cost ()
Percent Frequency
Parts Frequency
2 13 16
7 7 5 50
4 26 32 14
14 10 100
50-59 60-69 70-79 80-89
90-99 100-109
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Graphical Summary Histogram
Tune-up Parts Cost
Frequency
Parts Cost ()
50-59 60-69 70-79 80-89 90-99 100-110
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Numerical Descriptive Statistics

• The 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).

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1.5 Statistical Inference
Population
- the set of all elements of interest in a
particular study
Sample
- a subset of the population
Statistical inference
- the process of using data obtained from a
sample to make estimates and test hypotheses
about the characteristics of a population
Census
- collecting data for a population
Sample survey
- collecting data for a sample
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Process of Statistical Inference
1. Population consists of all tune-ups.
Average cost of parts is unknown.
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.
4. The sample average is used to estimate the
population average.
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1.6 Computers and Statistical Analysis

• Statistical analysis often involves working with
  large amounts of data.
• Computer software is typically used to conduct
  the analysis.
• Statistical software packages such as Microsoft
  Excel and Minitab are capable of data management,
  analysis, and presentation.
• Instructions for using Excel and Minitab are
  provided in chapter appendices.

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End of Chapter 1