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91Ó°ÊÓ

Indicate which of the following variables are quantitative and which are qualitative. a. Number of persons in a family b. Color of a car c. Marital status of a person d. Time to commute from home to work e. Number of errors in a person's credit report

Short Answer

Expert verified
a. Quantitative, b. Qualitative, c. Qualitative, d. Quantitative, e. Quantitative

Step by step solution

01

Identify the Type of Data for the Number of Persons in a Family

The number of persons in a family can be counted and measured on a numerical scale. Therefore, this variable is quantitative.
02

Identify the Type of Data for the Color of a Car

The color of a car is non-numerical and represents a type or category. This makes it a qualitative variable.
03

Identify the Type of Data for the Marital Status of a Person

The marital status of a person refers to a nominal category such as married, single, divorced or widowed. Thus, it is a qualitative variable.
04

Identify the Type of Data for the Time to Commute from Home to Work

The time it takes for a person to commute from home to work can be measured on a numerical scale in units such as minutes or hours. This variable is, therefore, quantitative.
05

Identify the Type of Data for the Number of Errors in a Person's Credit Report

The number of errors in a person's credit report can be measured numerically. Hence it is a quantitative variable.

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Key Concepts

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

Quantitative Data
Quantitative data refers to information that can be measured and expressed numerically. This type of data is beneficial because it allows us to quantify variables and perform mathematical operations on them. For example, the number of persons in a family or the number of errors in a credit report are quantitative data types. Both examples can be counted and analyzed to find averages or other statistical measures. Another example is the time taken to commute from home to work, which can be recorded in minutes or hours.
Quantitative data can be further categorized into discrete and continuous data:
  • Discrete data consists of distinct, separate values, often counted in whole numbers, like the number of persons in a family.
  • Continuous data, on the other hand, can take any value within a range and can be measured with more precision, such as time or weight.
Understanding quantitative data is crucial as it forms the basis for most statistical analyses, helping draw meaningful conclusions from data.
Qualitative Data
Qualitative data, sometimes known as categorical data, is used to describe characteristics or categories and is not numerical in nature. This type of data helps in understanding the qualities or properties of a variable rather than its numerical value. Consider the color of a car or the marital status of a person; both are qualitative data because they describe categories or states.
Qualitative data can be further divided into two main types:
  • Nominal data represents categories without any intrinsic order, like car colors or marital status (e.g., married, single).
  • Ordinal data represents categories with a meaningful order but without a specific numerical difference between them, such as satisfaction levels (e.g., satisfied, neutral, unsatisfied).
While qualitative data cannot be used for mathematical computations, it is crucial for providing context and depth to statistical descriptions and analyses.
Data Types in Statistics
Understanding the different types of data in statistics is vital for choosing the correct analysis methods and drawing valid conclusions. The two primary data types are quantitative and qualitative data, each serving unique purposes and requiring different approaches.
Quantitative data provides numerical insight and enables statistical calculations, forecasting, and trend analysis. This data can further be explored using graphical representation like histograms, pie charts, or scatter plots to easily interpret the numbers involved.
Qualitative data, on the other hand, enriches datasets by adding texture and detail through categories and descriptions, supporting the appreciation of patterns and insights not measurable by numbers alone. Visualization for qualitative data often uses bar charts or pie charts to show proportions or frequencies of different categories.
Understanding these data types is essential for any statistical work as it informs the choice of statistical tests and methodologies to apply, ensuring data is used to its fullest potential.

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Most popular questions from this chapter

Explain whether each of the following constitutes data collected from a population or a sample. a. The number of pizzas ordered on Fridays during 2012 at all of the pizza parlors in your town. b. The dollar values of auto insurance claims filed in 2012 for 200 randomly selected policies. c. The opening price of each of the 500 stocks in the S\&P 500 stock index on January 3, 2012 . d. The total home attendance for each of the 18 teams in Major League Soccer during the 2012 season. e. The living areas of 35 houses listed for sale on March 7,2012 in Chicago, Illinois.

Indicate whether each of the following constitutes data collected from a population or a sample. a. A group of 25 patients selected to test a new drug b. Total items produced on a machine for each year from 1995 to 2012 c. Yearly expenditures on clothes for 50 persons d. Number of houses sold by each of the 10 employees of a real estate agency during 2012

Explain whether each of the following constitutes data collected from a population or a sample. a. Opinions on a certain issue obtained from all adults living in a city. b. The price of a gallon of regular unleaded gasoline on a given day at each of 28 gas stations in the Miami, Florida, metropolitan area. c. Credit card debts of 100 families selected from a given city. d. The percentage of all U.S. registered voters in each state who voted in the 2012 Presidential election. e. The number of left-handed students in each of 50 classes selected from a given university.

The number of pizzas delivered to a college campus on six randomly selected nights is \(48,103,95\), 188,286, and 136, respectively. Let \(x\) denote the number of pizzas delivered to this college campus on any given night. Find: a. \(\Sigma x\) b. \((\Sigma x)^{2} \quad\) c. \(\Sigma x^{2}\)

Explain the meaning of the following terms. a. Quantitative variable b. Qualitative variable \(\underline{\text { c. }}\) Discrete variable d. Continuous variable e. Quantitative data f. Qualitative data

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