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Chapter 1: Problem 32

Determine whether the quantitative variable is discrete or continuous. Weight of a randomly selected hog

Short Answer

Expert verified
Continuous

Step by step solution

01

Define Discrete and Continuous Variables

A variable is discrete if it can only take specific, separate values (often integers), and there are gaps between the possible values. Continuous variables, on the other hand, can take any value within a given range and have no gaps between possible values.
02

Identify the Variable in Question

The variable in question is the 'weight of a randomly selected hog.'
03

Determine the Nature of Weight

Weight can take any value within a certain range and can be measured with varying degrees of precision. This means there are no gaps between the possible weight values of a hog. For example, a hog can weigh 200.1 pounds, 200.15 pounds, 200.155 pounds, and so on.
04

Classify the Variable

Since weight can take on any value within a range and is not restricted to specific separate values, it is a continuous variable.

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Key Concepts

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

discrete variables
Discrete variables can only take on specific, separate values. Think of them as counting numbers. There are gaps between these values, and you can't have a value in between. For example, the number of students in a class can be 20, 21, or 22, but it cannot be 20.5. These variables are often integers and are very useful in situations where only whole units matter. Here are some characteristics of discrete variables:
  • Specific and distinct values
  • Gaps between values
  • Typically counts or categories
  • Examples: number of pets, number of books, test grades
continuous variables
Continuous variables, on the other hand, can take any value within a given range. There are no gaps between the possible values they can assume. You can measure them to varying degrees of precision, making them very flexible for detailed analysis. For instance, the weight of a hog is a continuous variable because it can be 200.1 pounds, 200.15 pounds, and so on. Here are some characteristics of continuous variables:
  • Range of values without gaps
  • Can be measured to any level of precision
  • Often associated with measurements
  • Examples: height, weight, temperature, time
quantitative variables
Quantitative variables are numerical and can be measured or counted. They are different from qualitative (or categorical) variables, which describe attributes or qualities. Quantitative variables can be further classified into discrete and continuous variables. Whether you are counting discrete items or measuring continuous quantities, both fall under the umbrella of quantitative variables. Here are some characteristics of quantitative variables:
  • Numerical values
  • Can be discrete or continuous
  • Allow for arithmetic operations
  • Examples: number of pages, distance traveled, monthly income, time spent studying
statistical classification
Statistical classification involves categorizing data based on certain criteria. When it comes to variables, the main distinction is between qualitative and quantitative. Quantitative variables can be further divided into discrete and continuous types. Proper classification helps in choosing the right statistical methods for data analysis. Here are some basic steps in statistical classification:
  • Identify the variable
  • Determine if it is qualitative or quantitative
  • If quantitative, check if it is discrete or continuous
  • Use appropriate statistical tools based on classification
Proper classification leads to more accurate analysis and better decision-making. It also ensures that the data is handled correctly, providing meaningful insights.

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Most popular questions from this chapter

For the studies in Problems \(45-50,\) (a) identify the research objective, (b) identify the sample, (c) list the descriptive statistics, and (d) state the conclusions made in the study. The Mozart Effect Researchers at the University of California, Irvine, wished to determine whether "music cognition and cognitions pertaining to abstract operations such as mathematical or spatial reasoning" were related. To test the research question, 36 college students listened to Mozart's Sonata for Two Pianos in D Major, K488, for 10 minutes and then took a spatial reasoning test using the Stanford-Binet intelligence scale. The same students also took the test after sitting in a room for 10 minutes in complete silence. Whether the student experienced Mozart first or silence first was randomly determined. The average score on the test following the Mozart piece was \(119,\) while the average test score following the silence was 110. The researchers concluded that subjects performed better on abstract and spatial reasoning tests after listening to Mozart. (Source: "Music and Spatial Performance," Frances H. Rauscher et al.; Nature 365,14 October 1993: 611 )

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