Introduction to Statistics

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Statistics Alan D. Smith ROBERT MORRIS
UNIVERSITY
Alan D. Smith
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What is Statistics?
Chapter 1
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TODAYs GOALS

• DEFINE STATISTICS.
• CITE SOME USES OF STATISTICS IN BUSINESS AND
  OTHER AREAS.
• EXPLAIN WHAT IS MEANT BY DESCRIPTIVE STATISTICS
  AND INFERENTIAL STATISTICS.
• DISTINGUISH BETWEEN NOMINAL, ORDINAL, INTERVAL
  AND RATIO LEVELS OF MEASUREMENT.

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WHAT IS MEANT BY STATISTICS?

• Statistics is the science of collecting,
  organizing, presenting, analyzing, and
  interpreting numerical data for the purpose of
  assisting in making a more effective decision.
• WHO USES STATISTICS?
• Statistical techniques are used extensively by
  marketing, accounting, quality control,
  consumers, professional sports people, hospital
  administrators, educators, politicians,
  physicians, etc.

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TYPES OF STATISTICS

• Descriptive Statistics These are statistical
  methods used to describe data that have been
  collected.
• EXAMPLES According to J. D. Powers, Lexus LS400
  owners reported 32 problems per 100 cars during
  1994. The statistic 32 describes the number of
  problems out of every 100 cars.
• A Gallup poll found that 49 of the people in a
  survey knew the name of the first book of the
  Bible. The statistic 49 describes the number out
  of every 100 persons who knew the answer.

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TYPES OF STATISTICS (continued)

• Inferential Statistics These are statistical
  methods used to find out something about a
  population, based on a 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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Examples of Inferential Statistics

• TV networks constantly monitor the popularity of
  their programs by hiring Nielsen and other
  organizations to sample the preferences of TV
  viewers.
• The accounting department of a large firm will
  select a sample of the invoices to check for
  accuracy for all the invoices of the company.
• Wine tasters sip a few drops of wine to make a
  decision with respect to all the wine waiting to
  be released for sale.

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TYPES OF VARIABLES

• Qualitative or Attribute variable when the
  characteristic or variable being studied is
  categorical or non-proportional.
• EXAMPLES Gender (male, female), religious
  affiliation, type of automobile owned, state of
  birth, eye color, etc.
• Quantitative variable when the variable can be
  reported non-categorical or proportional.
• EXAMPLES Balance in your checking account,
  salaries of faculty members, number of children
  in a family etc.

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TYPES OF VARIABLES (continued)

• Quanitative variables can be classified as either
  discrete or continuous.
• Discrete Variables can only assume certain
  values and there are usually gaps between the
  values.
• EXAMPLE The number of bedrooms in a house (1, 2,
  3, ..., etc.).
• Continuous Variables can assume any value within
  a specific range.
• EXAMPLE The time it took to fly from New York to
  Guyana (South America).

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SUMMARY OF TYPES OF VARIABLES
Data
Qualitative or attribute
Quantitative or numerical
Type of car owned. Color of pens.
Discrete
Continuous
Number of children.
Time taken for an exam.
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SOURCES OF STATISTICAL DATA

• Researching problems involving topics such as
  crime, health, imports and exports, production,
  hourly wages etc. generally requires published
  data. Statistics on these and information on
  thousands of other topics can be found in
  published articles, journals, magazines, WWW.
• Published data are not always available on a
  given subject. In such cases, information will
  have to be collected and analyzed. One way of
  collecting data is through questionnaires.

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Conclusion?

• Missed Days of Work

Percent of Total Man-Days in Qtr
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LEVELS OF MEASUREMENT

• The four general types, or levels, of measurement
  are nominal, ordinal, interval, and ratio.
• NOMINAL LEVEL (SCALED) Data that can only be
  classified into categories and cannot be arranged
  in an ordering scheme.
• EXAMPLES Eye color (blue, brown, black etc.)
  Gender (male, female) Religious affiliations
  (Hindu, Catholic, Jewish, etc.).

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LEVELS OF MEASUREMENT ( terms)

• Mutually exclusive When an individual, object,
  or measurement is included in only one category,
  then they are mutually exclusive. For example -
  eye color, gender (male, female), etc.
• Can only appear in one category
• Exhaustive When each individual, object, or
  measurement must appear in one category, then
  they are exhaustive. For example - religion.
• Must appear in at least one category
• Mutually Exclusive and Exhaustive?

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LEVELS OF MEASUREMENT (continued)

• ORDINAL LEVEL This involves data that may be
  arranged in some order, but differences between
  data values cannot be determined or are
  meaningless.
• EXAMPLE During a taste test of 4 colas, cola 3
  was ranked number 1, cola 2 was ranked number 2,
  cola 1 was ranked number 3, and cola 4 was ranked
  number 4.
• Cola 3 is not four times better than cola 4

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LEVELS OF MEASUREMENT (continued)

• INTERVAL LEVEL This is similar to the ordinal
  level, with the the additional property that
  meaningful amounts of differences between data
  values can be determined. There is no natural
  zero point.
• EXAMPLE Temperature on the Fahrenheit scale.
  Differences can be computed and remain constant.
• 100 degrees is not twice as hot as 50 degrees

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LEVELS OF MEASUREMENT (continued)

• RATIO LEVEL This is the interval level with an
  inherent zero starting point. Differences and
  ratios are meaningful for this level of
  measurement.
• EXAMPLES Heights of the NBA players Money etc.
• 100 dollars is twice as much as 50 dollars
• 100 dollars is 50 more than 50 dollars