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Chapter 1: Problem 23

Determine whether the quantitative variable is discrete or continuous. Goals scored in a season by a soccer plaver

Short Answer

Expert verified
The variable is discrete because it takes on countable, whole number values.

Step by step solution

01

Understand Discrete and Continuous Variables

A discrete variable is one that can take on a countable number of values. These values are often integers. A continuous variable, on the other hand, can take on an infinite number of values within a given range, and these can include fractions and decimals.
02

Identify the Nature of the Variable

Examine the variable provided: goals scored in a season by a soccer player. Assess if this variable can take on only specific, countable values, or if it can take on any value within a range.
03

Evaluate the Variable

Goals scored in a season by a soccer player can take on countable, distinct values like 0, 1, 2, 3, etc. It cannot be a fraction or decimal because a player cannot score a part of a goal.
04

Conclusion

Since the goals scored in a season by a soccer player can only be whole numbers and not fractions or decimals, it is a discrete variable.

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Key Concepts

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

Quantitative Variables
Quantitative variables are those that can be measured and expressed numerically. They represent quantities and allow us to perform mathematical operations on the data. For example, height, weight, and temperature are all quantitative variables.
Quantitative variables can be further divided into two main types: discrete and continuous. Understanding these differences is key to correctly categorizing data in exercises and real-world applications.
Discrete Variables
Discrete variables are a type of quantitative variable that can take on a countable number of distinct values. These values are usually whole numbers and can often be listed out or enumerated.
Examples of discrete variables include:
  • The number of students in a classroom
  • The number of cars in a parking lot
  • The number of goals scored by a player in a season
In the given exercise, 'goals scored in a season by a soccer player' is a clear example of a discrete variable, as goals can only be whole numbers like 0, 1, 2, etc.
Continuous Variables
Continuous variables are another type of quantitative variable. Unlike discrete variables, they can take on an infinite number of values within a given range. This means that continuous variables can include any value, often including fractions and decimals.
Examples of continuous variables include:
  • Height of a person, which can be measured in units like meters or feet, and can include values like 1.75 meters
  • Weight of an object, which can be measured in kilograms or pounds, and can include values like 70.5 kilograms
  • Temperature, which can include decimal values like 37.2 degrees Celsius
A key characteristic of continuous variables is that between any two values, there can be another value. For instance, between 1.6 and 1.7 meters, there are infinite possible values like 1.61, 1.62, etc.
This property allows continuous variables to provide more precise and detailed measurements compared to discrete variables.

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Most popular questions from this chapter

Is a television (TV) in the bedroom associated with obesity? Researchers questioned 379 twelve-year old adolescents and concluded that the body mass index (BMI) of the adolescents who had a TV in their bedroom was significantly higher than the BMI of those who did not have a TV in their bedroom. Source: Christelle Delmas, Carine Platat, Brigette Schweitzer, Aline Wagner, Mohamed Oujaa, and Chantal Simon. "Association Between Television in Bedroom and Adiposity Throughout Adolescence," Obesity, \(15: 2495-2503,2007\) (a) Why is this an observational study? What type of observational study is this? (b) What is the response variable in the study? What is the explanatory variable? (c) Can you think of any lurking variables that may affect the results of the study? (d) In the report, the researchers stated, "These results remain significant after adjustment for socioeconomic status." What does this mean? (e) Can we conclude that a television in the bedroom causes a higher body mass index? Explain.

The survey has bias. (a) Determine the type of bias. (b) Suggest a remedy. A polling organization conducts a study to estimate the percentage of households that speaks a foreign language as the primary language. It mails a questionnaire to 1023 randomly selected households throughout the United States and asks the head of household if a foreign language is the primary language spoken in the home. Of the 1023 households selected, 12 responded.

Gallup News Service conducted a survey of 1017 American adults aged 18 years or older, September \(4-7,2014 .\) The respondents were asked, "Of every tax dollar that goes to the federal government in Washington, D.C. how many cents of each dollar would you say are wasted?" Of the 1017 individuals surveyed, \(35 \%\) indicated that 51 cents or more is wasted. Gallup reported that \(35 \%\) of all adult Americans 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of \(4 \%\) and a \(95 \%\) level of confidence. (a) What is the research objective? (b) What is the population? (c) What is the sample? (d) List the descriptive statistics. (e) What can be inferred from this survey?

Researchers wanted to evaluate whether ginkgo, an over-the-counter herb marketed as enhancing memory, improves memory in elderly adults as measured by objective tests. To do this, they recruited 98 men and 132 women older than 60 years and in good health. Participants were randomly assigned to receive ginkgo, 40 milligrams (mg) 3 times per day, or a matching placebo. The measure of memory improvement was determined by a standardized test of learning and memory. After 6 weeks of treatment, the data indicated that ginkgo did not increase performance on standard tests of learning, memory, attention, and concentration. These data suggest that, when taken following the manufacturer's instructions, ginkgo provides no measurable increase in memory or related cognitive function to adults with healthy cognitive function. (a) What type of experimental design is this? (b) What is the population being studied? (c) What is the response variable in this study? (d) What is the factor that is set to predetermined levels? What are the treatments? (e) Identify the experimental units. (f) What is the control group in this study? (g) Draw a diagram similar to Figure \(7,8,\) or 10 to illustrate the design.

Determine the level of measurement of each variable. Time of day measured in military time
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