Chapter 1 Data and Statistics

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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

• Statistics is the process of data collection,
  organizing, analyzing the data, interpertation
  and make decisions.
• Accounting
• Public accounting firms use statistical sampling
  procedures when conducting audits for their
  clients.
• Finance
• Financial analysts use a variety of statistical
  information, including price-earnings ratios and
  dividend yields, to guide their investment
  recommendations.
• Marketing
• 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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Applications in Business and Economics

• Production
• A variety of statistical quality control charts
  are used to monitor the output of a production
  process.
• Economics
• Economists use statistical information in making
  forecasts about the future of the economy or some
  aspect of it.

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Why Study Statistics?

• Numerical information is everywhere
• Statistical techniques are used to make decisions
  that affect our daily lives
• The knowledge of statistical methods will help
  you to understand how decisions are made and give
  you a better understanding of how they affect
  you.
• No matter what line of work you select, you will
  find yourself faced with decisions where an
  understanding of data analysis is helpful.
• Some examples of the need for data collection.
• Research analysts evaluate many facets of a
  particular stock before making a buy or sell
  recommendation.
• The marketing department Managers must make
  decisions about the quality of their product or
  service.

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What is Meant by Statistics?

• In the more common usage, statistics refers to
  numerical information.
• Examples the average starting salary of college
  graduates, the number of deaths due to alcoholism
  last year etc.
• We often present statistical information in a
  graphical form for capturing reader attention.

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Types of Statistics

• Descriptive Statistics - methods of organizing,
  summarizing, and presenting data in an
  informative way.
• Inferential Statistics A decision, estimate,
  prediction, or generalization about a population,
  based on a sample.

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Population versus Sample

• A population is a collection of all possible
  individuals, objects, or measurements of
  interest.
• A sample is a portion, or part, of the population
  of interest

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Data

• 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.
  E.g.,
• IBMs sales revenue is 100 bn. stock price 80.
• The data collected in a particular study are
  referred to as the data set. E.g.,
• The sales revenue and stock price data for a
  number of firms including IBM, Dell, Apple, etc.

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Elements, Variables, and Observations

• The elements are the entities on which data are
  collected. E.g.,
• IBM, Dell, Apple, etc. in the previous setting.
• A variable is a characteristic of interest for
  the elements. E.g.,
• Sales revenue, stock price (of a company)
• The set of measurements collected for a
  particular element is called an observation.
• Sales revenue, stock price for 2003

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Scales of Measurement

• 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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Scales of Measurement

• Nominal
• data that is classified into categories and
  cannot be arranged in any particular order. A
  numeric code may be used. The Nominal Scales
  Categorize Individuals or Groups And This Scale
  Measure The Percentage Response E.G. Male-
  Female, Pakistani-American
• 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
• similar to the nominal level, with the additional
  property that meaningful amounts of differences
  between data values can be determined. It
  categorizes and ranks the variables according to
  the preferences e.g. from best to worst, first to
  last, a numeric code may be used.
• e.g. rank job characteristics
• Example
• Students of a university are classified by
  their class standing using a nonnumeric label
  such as Freshman, Junior, Senior.
• Alternatively, a numeric code could be used
  for the class standing variable (e.g. 1 denotes
  Freshman, 2 denotes, Junior and so on).

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Scales of Measurement

• Interval
• The data have the properties of ordinal and
  interval between observations is expressed in
  terms of a fixed unit of measure. Preferences on
  a 5/7 point scale. It also measures the magnitude
  of the differences in the preferences among the
  individuals. Interval data are always numeric.
• Example
• strongly disagree, disagree, neither agree nor
  disagree, agree, strongly agree etc.

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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. This
  scale must contain a zero value that indicates
  that nothing exists for the variable at the zero
  point.
• Example
• Variables such as distance, height, weight, and
  time use the ratio scale.

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Scales of Measurement

• Ratio scales used when exact numbers are called
  for e.g. how many orders do you operate?
• Interval scale used for responses to various
  items on 5/7 points use of stats measures as
  ratio scale, a. mean, stand. deviation.
• Ordinal scale for preference in use, stats
  measures are median, range, rank order
  correlations
  
• Nominal scale used for personal data

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Types of Variables

• A. Qualitative variable - the characteristic
  being studied is nonnumeric.
• EXAMPLES Gender, religious affiliation, type of
  automobile owned, eye color are examples.
• use either the nominal or ordinal scale of
  measurement.
• B. Quantitative variable - information is
  reported numerically.
• EXAMPLES balance in your account, minutes
  remaining in class, or number of children in a
  family.

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Quantitative Data

• 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.
• Quantitative data are always numeric.
• Arithmetic operations (e.g., , -) are meaningful
  only with quantitative data.

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Summary of Types of Variables
LO4
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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
• Time series data are collected over several time
  periods.
• Example 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.
• Substantial amounts of business and economic data
  are available from organizations that specialize
  in collecting and maintaining data.
• 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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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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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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Example Hudson Auto Repair

• 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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Example Hudson Auto Repair

• Graphical Summary (Histogram)

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16
14
12
Frequency
10
8
6
4
2
Parts Cost ()
50 60 70 80 90 100
110
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Example Hudson Auto Repair

• 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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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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Example Hudson Auto Repair

• 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
cost of 79 per tune-up.
4. The value of the sample average is used to
make an estimate of the population average.
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End of Chapter 1