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Chapter 1: Problem 19

Classify the variable as qualitative or quantitative. Grams of carbohydrates in a doughnut

Short Answer

Expert verified
Quantitative.

Step by step solution

01

- Understand the definitions

Qualitative variables are descriptive and categorical, meaning they describe qualities or characteristics. Quantitative variables are numerical and can be measured or counted.
02

- Identify the nature of the variable

The variable in question is 'Grams of carbohydrates in a doughnut'.
03

- Determine if the variable is numerical or descriptive

Since 'Grams of carbohydrates in a doughnut' is measured in grams, it is a numerical value.
04

- Classify the variable

Because it is a numerical value that measures an amount, 'Grams of carbohydrates in a doughnut' is a quantitative variable.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

qualitative variables
Qualitative variables, also known as categorical variables, describe qualities or characteristics of an observation. They represent data that can be separated into distinct categories that do not have a specific numerical value attached to them. For example,
  • Types of doughnuts (glazed, chocolate, cream-filled)
  • Colors of a car (red, blue, green)
  • Brands of cereal (Kellogg's, General Mills, Post)
These variables are crucial when it comes to statistics because they allow us to classify and group items based on shared features or categories. An important aspect of qualitative variables is that even though they describe non-numerical attributes, they can sometimes be converted into numerical form for analysis purposes by assigning numbers to categories, but this does not make them quantitative.
quantitative variables
Quantitative variables, in contrast to qualitative ones, are numeric and represent measurable quantities. These variables put numbers to the traits being studied, allowing for a wide range of statistical analyses and comparisons. Examples include:
  • Grams of carbohydrates in a doughnut
  • Height of students in a class
  • Number of books in a library
Quantitative variables are further divided into two types: discrete and continuous. Discrete variables are countable, such as the number of students in a classroom. Continuous variables can take any value within a given range, like the amount of time taken to run a marathon. Knowing whether a variable is quantitative or qualitative is critical for choosing the appropriate statistical method and analysis.
measurement
Measurement refers to the process of assigning numbers or labels to variables based on certain rules. There are different levels of measurement that are important to understand:
  • Nominal scale: The simplest level which categorizes data without any numerical meaning, like types of fruit (apples, oranges).
  • Ordinal scale: This adds a rank order to the categories but does not determine the magnitude of the difference between them, like class grades (A, B, C).
  • Interval scale: This includes ordered categories that are equal intervals apart, but there is no true zero point, like the temperature in Celsius.
  • Ratio scale: This has all the properties of an interval scale, with the addition of a meaningful zero point, like weight or height.
Understanding these scales is essential because they determine the type of statistical analysis that can be applied. For instance, calculating a mean is meaningful in an interval or ratio scale but not in a nominal or ordinal scale.

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Most popular questions from this chapter

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