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Chapter 2: Problem 174

Identify each of the following as examples of (1) attribute (qualitative) or ( 2 ) numerical (quantitative) variables. a. The amount of weight lost in the past month by a person following a strict diet b. Batting averages of Major League Baseball players c. Decisions by the jury in felony trials d. Sunscreen usage before going in the sun (always, often, sometimes, seldom, never) e. Reason a manager failed to act against an employee's poor performance

Short Answer

Expert verified
a. Numerical (Quantitative) \n b. Numerical (Quantitative) \n c. Attribute (Qualitative) \n d. Attribute (Qualitative) \n e. Attribute (Qualitative)

Step by step solution

01

Classify the Weight Loss Variable

Begin by identifying the type of variable for the amount of weight lost in the past month by a person following a strict diet. As this variable is presented in a numerical form, it's a numerical (quantitative) variable, because it represents a quantity with meaningful size or magnitude.
02

Classify the Batting Average Variable

Next, consider the batting averages of Major League Baseball players. Batting average is represented with a numerical value that holds a meaningful size or magnitude, thus, it is classified as a numerical (quantitative) variable.
03

Classify the Jury Decision Variable

Moving on to the decisions by the jury in felony trials, as jury decisions are categories (guilty, not guilty, etc,), this is classified as an attribute (qualitative) variable.
04

Classify the Sunscreen Usage Variable

Sunscreen usage before going in the sun (always, often, sometimes, seldom, never). These options do not suggest a quantity or magnitude but a frequency of an activity, indicating that it is an attribute (qualitative) variable.
05

Classify the Reason for Inaction Variable

Lastly, consider the reason a manager failed to act against an employee's poor performance. Reasons are words or phrases representing certain categories, therefore we classify this as an attribute (qualitative) 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 the types of variables that deal with numbers. These variables tell us about the quantity, size, or magnitude of something. For instance, the amount of weight lost by an individual following a diet or the batting averages of baseball players fit into this category. This is because both of these are measured in numerical terms that convey meaningful information.

Quantitative data usually comes in two forms:
  • Discrete: These are countable data points, like the number of students in a class.
  • Continuous: These can take any value, such as the weight of a person or the temperature of a cup of coffee.
Understanding these variables is essential in statistics, as they help make sense of numerical data, enabling precise calculations and analysis.
Qualitative Variables
Qualitative variables, also known as categorical variables, describe non-numeric aspects of data. They categorize or label data points without involving any numbers. Examples include jury decisions, such as 'guilty' or 'not guilty,' and sunscreen usage described through terms like 'always' or 'never.'

With qualitative variables, it's important to recognize the use of labels or categories:
  • Nominal: These have different categories without any sort of order, like color names or types of movies.
  • Ordinal: These have a clear order or ranking, such as 'often' vs. 'seldom.'
These variables provide a way to capture and analyze information that does not need numerical representation but is still crucial for drawing insights out of data.
Data Classification
Classifying data is a foundational step in statistics that provides structure to raw information, allowing us to analyze it effectively. At a basic level, data is classified into either quantitative or qualitative categories.

A well-organized system of data classification helps researchers and analysts keep track of variables and analyze them accurately.
  • Determining appropriate methods: Data classification influences the statistical methods applied, such as mean and median for quantitative data versus frequency counts for qualitative data.
  • Predicting Outcomes: Proper classification allows for thorough analysis, which aids in predicting and explaining outcomes more reliably.
Familiarity with data classification saves time and enhances the reliability of any statistical analysis.
Educational Problems
Educational problems often arise from misunderstandings related to data handling and statistical concepts. Common challenges include improper identification of variable types, which can lead to inaccurate data analysis.

Some typical issues faced by students include:
  • Mistaking qualitative for quantitative variables, or vice versa.
  • Applying incorrect statistical techniques based on variable classification.
  • Confusion in interpreting results due to lack of understanding of data types.
By fostering a solid grasp of variable identification and classification, educators can equip students with the skills to overcome these hurdles, resulting in more effective learning and application of statistical concepts.
Statistical Analysis
Statistical analysis is the backbone of turning data into actionable insights. Through statistical analysis, variables are closely examined to establish patterns and trends that inform decision-making processes. The key steps include data collection, classification, and analysis.

Each analysis step benefits significantly from understanding the type of variables involved:
  • Deciding on the appropriate analytical methods.
  • Determining how to interpret outcomes accurately.
  • Ensuring results are meaningful and reliable.
An effective statistical analysis hinges on properly identifying and classifying variables, leading to better decision-making based on well-analyzed data.

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Most popular questions from this chapter

Henry Cavendish, an English chemist and physicist \((1731-1810),\) approached many of his experiments using quantitative measurements. He was the first to accurately measure the density of the Earth. Following are 29 measurements (ranked for your convenience of the density of the Earth done by Cavendish in 1798 using a torsion balance. Density is presented as a multiple of the density of water. (Measurements are in \(\left.\mathrm{g} / \mathrm{cm}^{3} .\right)\) $$\begin{array}{llllllllll} \hline 4.88 & 5.07 & 5.10 & 5.26 & 5.27 & 5.29 & 5.29 & 5.30 & 5.34 & 5.34 \\ 5.36 & 5.39 & 5.42 & 5.44 & 5.46 & 5.47 & 5.50 & 5.53 & 5.55 & 5.57 \\ 5.58 & 5.61 & 5.62 & 5.63 & 5.65 & 5.68 & 5.75 & 5.79 & 5.85 & \\ \hline \end{array}$$ a. Describe the data set by calculating the mean, median, and standard deviation. b. Construct a histogram and explain how it demonstrates the values of the descriptive statistics in part a. c. Find the 5 -number summary. d. Construct a box-and-whiskers display and explain how it demonstrates the values of the descriptive statistics in part c. e. Based on the two graphs, what "shape" is this distribution of measurements? f. Assuming that Earth density measurements have an approximately normal distribution, approximately \(95 \%\) of the data should fall within 2 standard deviations of the mean. Is this true?

What kinds of financial transactions do you do online? Are you worried about your security? According to Consumer Internet Barometer, the source of a March \(25,2009,\) USA Today Snapshot titled "Security of online accounts," the following transactions and percent of people concerned about their online security were reported. $$\begin{array}{lc} \text { What } & \text { Percent } \\ \hline \text { Bankirg } & 72 \\ \text { Paying bills } & 70 \\ \text { Buying stocks, bords } & 62 \\ \text { Fling toxes } & 62 \\ \hline \end{array}$$ Prepare two bar graphs to depict the percentage data. Scale the vertical axis on the first graph from 50 to \(80 .\) Scale the second graph from 0 to \(100 .\) What is your conclusion concerning how the percentages of the four responses stack up based on the two bar graphs, and what would you recommend, if anything, to improve the presentations?

The speeds of 55 cars were measured by a radar device on a city street: $$\begin{array}{llllllllll} \hline 27 & 23 & 22 & 38 & 43 & 24 & 35 & 26 & 28 & 18 & 20 \\ 25 & 23 & 22 & 52 & 31 & 30 & 41 & 45 & 29 & 27 & 43 \\ 29 & 28 & 27 & 25 & 29 & 28 & 24 & 37 & 28 & 29 & 18 \\ 26 & 33 & 25 & 27 & 25 & 34 & 32 & 36 & 22 & 32 & 33 \\ 21 & 23 & 24 & 18 & 48 & 23 & 16 & 38 & 26 & 21 & 23 \\ \hline \end{array}$$ a. Classify these data into a grouped frequency distribution by using class boundaries \(12-18,18-24, \ldots\) \(48-54\) b. Find the class width. c. For the class \(24-30,\) find the class midpoint, the lower class boundary, and the upper class boundary. d. Construct a frequency histogram of these data.

Which \(x\) value has the lower position relative to the set of data from which it comes? \( \mathrm{A}: x=28.1, \text { where } \bar{x}=25.7 \text { and } s=1.8 \) \(\mathbf{B}: x=39.2,\) where \(\bar{x}=34.1\) and \(s=4.3\)

Your instructor and your class have made a deal on the exam just taken and currently being graded. If the class attains a mean score of 74 or better, there will be no homework on the coming weekend. If the class mean is 72 or below, then not only will there be homework as usual but all of the class members will have to show up on Saturday and do 2 hours of general cleanup around the school grounds as a community service project. There are 15 students in your class. Your instructor has graded the first 14 exams, and their mean score is \(73.5 .\) Your exam is the only one left to grade. a. What score must you get in order for the class to win the deal? b. What score must you get in order that the class will not have to do the community service work?
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