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Chapter 1 Data and Statistics

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Title: Chapter 1 Data and Statistics


1
Chapter 1 Data and Statistics
  • Applications in Business and Economics
  • Data
  • Data Sources
  • Descriptive Statistics
  • Statistical Inference

2
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.

3
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.

4
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.

5
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.

6
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.

7
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

8
Data
  • Elements, Variables, and Observations
  • Scales of Measurement
  • Qualitative and Quantitative Data
  • Cross-Sectional and Time Series Data

9
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.

10
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

11
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.

12
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).

13
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).

14
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.

15
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.

16
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

17
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.

18
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.

19
Summary of Types of Variables
LO4
20
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

21
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.

22
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.

23
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.

24
Descriptive Statistics
  • Descriptive statistics are the tabular,
    graphical, and numerical methods used to
    summarize data.

25
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.
26
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

27
Example Hudson Auto Repair
  • Graphical Summary (Histogram)

18
16
14
12
Frequency
10
8
6
4
2
Parts Cost ()
50 60 70 80 90 100
110
28
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).

29
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).

30
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.
31
End of Chapter 1
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