SECTION 1.2 TYPES OF DATA

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

Understand the structure of a typical data set Objective 1

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

Distinguish between qualitative and quantitative variables Objective 2

Qualitative and Quantitative Variables Variables can be divided into two types:  Qualitative Variables  Quantitative Variables Variables QualitativeQuantitative

Qualitative and Quantitative Variables Qualitative variables classify individuals into categories. Quantitative variables tell how much or how many of something there is.

Example Which of the following variables are qualitative and which are quantitative? (a) A person’s age (b) A person’s gender (c) The mileage (in miles per gallon) of a car (d) The color of a car

Solution The following variables are qualitative: A person’s gender. This is qualitative because it consists of the categories “male” and “female.” The color of a car. This is qualitative because it consists of the categories of different colors. The following variables are quantitative: A person’s age. This is quantitative because it tells how much time has elapsed since the person was born. The mileage of a car. This is quantitative because it tells how many miles a car will go on a gallon of gasoline.

Distinguish between ordinal and nominal variables Objective 3

Ordinal and Nominal Qualitative Variables Qualitative variables can be further divided into nominal variables and ordinal variables. Variables Qualitative NominalOrdinal Quantitative

Ordinal and Nominal Qualitative Variables Ordinal variables have a natural ordering. Nominal variables have no natural ordering.

Example Which of the following variables are ordinal and which are nominal? (a) State of residence (b) Gender (c) Letter grade in a statistics class (A, B, C, D, or F) (d) Size of soft drink ordered at a fast-food restaurant (small, medium, or large)

Solution Examples of ordinal variables include:  Letter grades in a Statistics class  The size of a soft drink (small, medium, large) Examples of nominal variables include:  State of residence  Gender

Distinguish between discrete and continuous variables Objective 4

Discrete and Continuous Quantitative Variables Quantitative variables can be further divided into discrete variables and continuous variables. Variables Qualitative NominalOrdinal Quantitative DiscreteContinuous

Discrete and Continuous Quantitative Variables Discrete variables are quantitative variables whose possible values can be listed. Continuous variables are quantitative variables that can take on any value in some interval.

Example Which of the following variables are discrete and which are continuous? (a) The age of a person at his or her last birthday (b) The height of a person (c) The number of siblings a person has (d) The distance a person commutes to work

Solution The following are examples of Discrete variables:  A person’s age at his or her last birthday  The number of siblings a person has The following are examples of Continuous variables:  A person’s height  The distance a person commutes to work

Do You Know… Structure of a data set? Difference between qualitative and quantitative variables? Difference between the types of qualitative variables? Difference between discrete and continuous variables?