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Chapter 6: Problem 4

Determine whether each of the following variables would best be modeled as continuous or discrete. a. The weight of a car in pounds b. The weight of a car in kilograms

Short Answer

Expert verified
Both the weight of a car in pounds and the weight of a car in kilograms would be modeled as continuous variables.

Step by step solution

01

Understand Discrete and Continuous Variables

Discrete variables are countable in a finite amount of time. For example, you can count the change in your pocket. You can count the money in your bank account. You can count the amount of hair on your head. Continuous variables, however, would (literally) take forever to count. In fact, you would get to 'forever' and never finish counting them. For example, measuring the weight of something gives a continuous data type because you could potentially measure with increasing accuracy without end.
02

Application to weight in pounds

Applying this understanding to the weight of a car in pounds, it is obvious that this will be a continuous variable, as a car's weight in pounds does not have to be a whole number - it can include decimal points, thus making measurements potentially infinite within a given range.
03

Application to weight in kilograms

Likewise, the weight of the car in kilograms would also be a continuous variable, as the weight does not have to be a whole number - it can include decimal points, again making measurements potentially infinite within a given range.

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Key Concepts

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

Statistical Modeling
Statistical modeling is a critical tool in understanding complex data. At its core, it involves the application of statistical methods to represent data in a mathematical framework. This is essential for analyzing and drawing meaningful conclusions from data.

It allows researchers to make predictions or understand relationships between variables. Models can be linear or nonlinear, simple or complex, depending on the data being analyzed and the questions being asked.
  • Purpose: To simplify real-world problems and predict future events based on data.
  • Process: Involves forming hypotheses, applying appropriate statistical techniques, and validating outcomes.
  • Outcome: Offers insights that facilitate decision-making and strategy formulation.
Understanding whether variables are continuous or discrete is integral to choosing the right statistical model, as each handles different types of data in unique ways.
Data Types
Data types are crucial for statistical analysis as they define the kind of operations that can be performed on the data. They describe the essential nature of the information within a dataset.

In statistics, the primary data types are:
  • Nominal: Data with categories without a specific order, like colors or types of animals.
  • Ordinal: Data with a specific order but without a consistent interval between them, like rankings.
  • Interval: Data with a consistent interval between values but no true zero, like temperature measured in Celsius.
  • Ratio: Data with a consistent interval and a true zero, like weight or height.
Distinguishing between continuous and discrete variables aids in the classification of data as interval or ratio, which influences the choice of statistical methods for analysis.
Variable Classification
Variable classification is foundational in the setup of any statistical analysis. It determines how data will be collected, analyzed, and interpreted.

Variables are broadly classified into two types:
  • Discrete Variables: These represent countable data, such as the number of students in a class. They have distinct, separate values.
  • Continuous Variables: These represent measurable data, which can take any value within a range, such as temperature or time.
Each type of variable serves different purposes in dataset analysis. For instance, continuous data allows for more in-depth statistical processes like calculating means or standard deviations.
Accurate variable classification is vital because it affects everything from data collection methods to the type of graphs and charts used for presentation. For the weight of a car, knowing it is a continuous variable informs how it should be recorded and analyzed for precise results.

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Most popular questions from this chapter

According to a study by the Colorado Department of Transportation, \(25 \%\) of Colorado drivers admit to using their cell phones to send texts while driving. Suppose two Colorado drivers are randomly selected. a. If the driver texts while driving, record a \(\mathrm{T}\). If not, record an \(\mathrm{N}\). List all possible sequences of Ts and Ns for the two drivers. b. For each sequence, find the probability that it will occur by assuming independence. c. What is the probability that both drivers text while driving? d. What is the probability that neither driver texts while driving? e. What is the probability that exactly one of the drivers texts while driving?

According to the Centers of Disease Control and Prevention, \(44 \%\) of U.S. households still had landline phone service. Suppose a random sample of 60 U.S. households is taken. a. Find the probability that exactly 25 of the households sampled still have a landline. b. Find the probability that more than 25 households still have a landline. c. Find the probability that at least 25 households still have a landline. d. Find the probability that between 20 and 25 households still have a landline.

Assume a standard Normal distribution. Draw a separate, well-labeled Normal curve for each part. a. Find an approximate \(z\) -score that gives a left area of \(0.7000\). b. Find an approximate \(z\) -score that gives a left area of \(0.9500\).

Quantitative SAT scores are approximately Normally distributed with a mean of 500 and a standard deviation of \(100 .\) On the horizontal axis of the graph, indicate the SAT scores that correspond with the provided \(z\) -scores. (See the labeling in Exercise 6.14.) Answer the questions using only your knowledge of the Empirical Rule and symmetry. a. Roughly what percentage of students earn quantitative SAT scores greater than \(500 ?\) i. almost all iii. \(50 \%\) \(\mathrm{v}\). about \(0 \%\) ii. \(75 \%\) iv. \(25 \%\) b. Roughly what percentage of students earn quantitative SAT scores between 400 and \(600 ?\) i. almost all iii. \(68 \%\) \(\mathrm{v}\). about \(0 \%\) ii. \(95 \%\) iv. \(34 \%\) c. Roughly what percentage of students earn quantitative SAT scores greater than \(800 ?\) i. almost all iii. \(68 \%\) \(\mathrm{v}\). about \(0 \%\) ii. \(95 \%\) iv. \(34 \%\) d. Roughly what percentage of students earn quantitative SAT scores les: than \(200 ?\) i. almost all iii. \(68 \%\) \(\mathrm{v}\). about \(0 \%\) ii. \(95 \%\) iv. \(34 \%\) e. Roughly what percentage of students earn quantitative SAT scores between 300 and \(700 ?\) i. almost all iii. \(68 \%\) v. \(2.5 \%\) ii. \(95 \%\) iv. \(34 \%\) f. Roughly what percentage of students earn quantitative SAT scores between 700 and 800 ? i. almost all iii. \(68 \%\) v. \(2.5 \%\) ii. \(95 \%\) iv. \(34 \%\)

The distribution of grade point averages GPAs for medical school applicants in 2017 were approximately Normal, with a mean of \(3.56\) and a standard deviation of \(0.34\). Suppose a medical school will only consider candidates with GPAs in the top \(15 \%\) of the applicant pool. An applicant has a GPA of \(3.71\). Does this GPA fall in the top \(15 \%\) of the applicant pool?
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