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What Are We Summarizing?

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  1. What Are We Summarizing? Lecture 11 Sections 4.1 – 4.2 Tue, Sep 20, 2005

  2. 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. 212. • How best to summarize Gender? • How best to summarize Age? • How best to summarize Blood Pressure?

  3. 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. • Examples: • Gender. • Questionnaire response, from strongly agree to strongly disagree.

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

  5. Continuous Variables • Continuous variable – The set of theoretically possible values of the variable forms a continuous set of real numbers. • Typically these are measured quantities: length, time, area, weight, etc. • Example: The length of time a student takes to complete a test. • Usually the noun does not have a plural form.

  6. Discrete Variables • Discrete variable – The set of theoretically possible values of the variable forms a set of isolated points on the number line. • Typically this is count data; a verbal description usually contains the phrase “the number of.” • Example: The number of students who completed the test within 40 minutes. • Usually the noun has a plural form.

  7. Discrete vs. Continuous • Some data may be considered to be either discrete or continuous. • Example: Time vs. Minutes. • How much time do I have for the test? • How many minutes do I have for the test? • Example: Money vs. Dollars. • How much money is in your pocket? • How many dollars are in your pocket? • In such cases, consider it to be continuous.

  8. Discrete vs. Continuous • Some data may be considered to be either discrete or continuous. • Example: Time vs. Minutes. • How much time do I have for the test? • How many minutes do I have for the test? • Example: Money vs. Dollars. • How much money is in your pocket? • How many dollars are in your pocket? • In such cases, consider it to be continuous.

  9. 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, … minutes. • Is that discrete or continuous?

  10. Let’s Do It! • Let’s do it! 4.1, p. 216 – What Type of Variable? • Think about it, p. 217.

  11. Parameters and Statistics • For quantitative variables (discrete or continuous), the most commonly used statistic is the average of the numbers. • Average weight of the postal packages. • For qualitative variables, the most commonly used statistic is the proportion of values in a specific category. • Proportion of packages that are in the light category.

  12. Qualitative or Quantitative? • Caution: Sometimes numbers are used merely as labels on the categories. That alone will not make the data quantitative.

  13. Qualitative or Quantitative? • On an opinion survey: • 1 = strongly disagree • 2 = disagree • 3 = neutral • 4 = agree • 5 = strongly agree • Is it legitimate to average the responses?

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