What Are We Summarizing Lecture 11 Sections 4

What Are We Summarizing? Lecture 11 Sections 4. 1 – 4. 2 Tue, Sep 20, 2005

What Are We Summarizing? There are various types of data. n How the data are summarized depends on the type of data. n See Data Set 1, p. 212. n How best to summarize Gender? n How best to summarize Age? n How best to summarize Blood Pressure? n

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

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

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

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

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

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

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

Let’s Do It! Let’s do it! 4. 1, p. 216 – What Type of Variable? n Think about it, p. 217. n

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

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

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