What Are We Summarizing?

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What Are We Summarizing?

• Lecture 14
• Secs. 4.1 4.2
• Mon, Feb 9, 2004

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What Are We Summarizing?

• There are various types of data.
• How the data are summarized depends on the type
  of data.
• See Data Set 1, p. 184.
• How best to summarize Gender?
• How best to summarize Age?
• How best to summarize Blood Pressure?

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Types of Variables

• Variables are either
• Qualitative, or
• Quantitative.

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Qualitative Variables

• Qualitative variable A variable whose values
  are not numerical, but can be divided into
  categories.
• The values of a qualitative variable may or may
  not have a natural order.
• Example Gender.
• Example Questionnaire response, from strongly
  agree to strongly disagree.

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Quantitative Variables

• Quantitative variable A variable whose values
  are numerical.
• A quantitative variable may be continuous or
  discrete.

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Continuous Variables

• Continuous variable The set of possible values
  of the variable forms a continuous set of real
  numbers.
• Example The length of time a student takes to
  complete a test.
• Typically these are measured quantities length,
  time, area, weight, etc.
• Modified by much.

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Discrete Variables

• Discrete variable The set of possible values of
  the variable forms a set of isolated points on
  the number line.
• Example The number of students who completed the
  test within 40 minutes.
• Typically this is count data a verbal
  description typically contains the phrase the
  number of.
• Modified by many.

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Discrete vs. Continuous

• Some data may be considered to be either discrete
  or continuous.
• Example Money.
• How much money do you have?
• How many dollars do you have?
• Other examples?

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Discrete vs. Continuous

• The distinction is based on the nature of the
  variable, not the manner in which it is measured
  or recorded.
• Example Measure the time it takes each student
  to finish a test, to the nearest minute.
• The possible times are 0, 1, 2, 3,
• Is that discrete or continuous?

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Let's Do It!

• Let's do it! 4.1, p. 187 What Type of Variable?
• The choice between qualitative and quantitative
  is based on how the observations are recorded.
• The choice between continuous and discrete is
  based on the nature of the quantity being
  measured.

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Think About It

• Think about it, p. 188.

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Assignment

• Page 191 Exercises 1 5.
• Page 249 Exercises 58 60.