1. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. T YPES OF D ATA Section 1.2

2. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Objectives 1. Understand the structure of a typical data set 2. Distinguish between qualitative and quantitative variables 3. Distinguish between ordinal and nominal variables 4. Distinguish between discrete and continuous variables

3. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. O BJECTIVE 1 Understand the structure of a typical data set

4. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Structure of a Data Set The values of the variables that we obtain are the data. The characteristics of the individuals about which we collect information are called variables. Information is collected on individuals. The information collected is called a data set. Data Set Individuals Variables Data

5. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. O BJECTIVE 2 Distinguish between qualitative and quantitative variables

6. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Qualitative and Quantitative Variables Variables can be divided into two types: Qualitative variables Classify individuals into categories Quantitative variables Tell how much or how many of something there is Variables Qualitative OrdinalNominal Quantitative DiscreteContinuous

7. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Example Which of the following variables are qualitative and which are quantitative? a) A person’s age This variable is quantitative because it tells how much time has elapsed since the person was born. b) A person’s gender This variable is qualitative because it consists of the categories “male” and “female”. c) The mileage of a car This variable is quantitative because it tells how many miles a car will go on a certain amount of gasoline. d) The color of a car This variable is qualitative because it consists of the categories of different colors.

8. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. O BJECTIVE 3 Distinguish between ordinal and nominal variables

9. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Ordinal and Nominal Qualitative variables can be further divided into ordinal and nominal variables: Ordinal variables Have a natural ordering Nominal variables Do not have a natural ordering Variables Qualitative OrdinalNominal Quantitative DiscreteContinuous

10. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Example Which of the following variables are ordinal and which are nominal? a) State of residence This variable is nominal because there is no natural ordering. b) Gender This variable is nominal because there is no natural ordering. c) Letter grade in a class (A, B, C, D, or F) This variable is ordinal because there is a natural ordering. For example, grades from best to worst are A, B, C, D, F. d) Size of a soft drink ordered at a fast-food restaurant This variable is ordinal because there is a natural ordering. For example, sizes may be small, medium, large, extra-large.

11. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. O BJECTIVE 4 Distinguish between discrete and continuous variables

12. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Discrete and Continuous Quantitative variables can be further divided into discrete and continuous variables: Discrete variables Possible values can be listed Continuous variables Can take on any value in some interval Variables Qualitative OrdinalNominal Quantitative DiscreteContinuous

13. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Example Which of the following variables are discrete and which are continuous? a) Age of a person at his or her last birthday This variable is discrete because a person’s age at his or her birthday can be listed. b) Height of a person This variable is continuous because height can take on any value in an interval. c) Number of siblings a person has This variable is discrete because the number of siblings can be listed. d) Distance a person commutes to work This variable is continuous because distance can take on any value in an interval.

14. Copyright © 2016 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. You Should Know… The structure of a data set How to distinguish between Qualitative and quantitative variables Ordinal and nominal variables Discrete and continuous variables