What Are We Summarizing? Lecture 14 Secs. 4.1 – 4.2 Mon, Feb 9, 2004

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?

Types of Variables Variables are either Qualitative, or Quantitative.

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.

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

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.”

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.”

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?

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?

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.

Think About It Think about it, p. 188.

Assignment Page 191: Exercises 1 – 5. Page 249: Exercises 58 – 60.