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Chapter 1: Problem 13

Classify each of the following variables as either categorical or numerical. For those that are numerical, determine whether they are discrete or continuous. a. Brand of computer purchased by a customer b. State of birth for someone born in the United States c. Price of a textbook d. Concentration of a contaminant (micrograms per cubic centimeter) in a water sample e. Zip code (Think carefully about this one.) f. Actual weight of coffee in a 1 -pound can

Short Answer

Expert verified
The variables are classified as follows: a. categorical, b. categorical, c. continuous numerical, d. continuous numerical, e. categorical, f. continuous numerical.

Step by step solution

01

Classifying a through d

Let's start by analyzing and classifying the varibles a through d. a. Brand of a computer is a categorical variable since brands cannot be quantified. b. State of birth for someone in the United States is also a categorical variable based on 50 distinct categories. c. Price of a textbook is a continuous numerical variable, it can take any positive real number. d. The concentration of a contaminant is also a numerical variable. More specifically, since the concentration can take any positive real value within a given range, it can be classified as continuous.
02

Classifying e and f

Let's proceed to classify the remaining variables, e and f. e. Zip code, though a number, is a categorical variable. This is because its numerical values don鈥檛 have a mathematical meaning, they serve merely as labels or codes. f. The actual weight of coffee in a 1-pound can is a numerical variable. Since, in theory, it could take any value between certain boundaries (probably slightly below and above one pound), it is a continuous variable. Note that the discretization of measures by the means' accuracy does not turn a numerically continuous variable into a discrete one.
03

Summary of Classified Variables

Finally, let's summarize all the variables identified and classified: Brand of computer - categorical; State of birth in the US - categorical; Price of a textbook - continuous numerical; Contaminant concentration - continuous numerical; Zip code - categorical; Actual weight of coffee - continuous numerical. Here it's important to note that the ability to correctly identify and classify variables is a fundamental first step in proper data analysis.

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