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Chapter 1: Problem 1

Fuel Economy. Here is a small part of a data set that describes the fuel economy in miles per gallon (mpg) of model year 2016 motor vehicles: The annual fuel cost is an estimate assuming 15,000 miles of travel a year (55\% city and \(45 \%\) highway) and an average fuel price. (a) What are the individuals in this data set? (b) For each individual, what variables are given? Which of these variables are categorical, and which are quantitative? In what units are the quantitative variables measured?

Short Answer

Expert verified
(a) The individuals are the 2016 model year vehicles. (b) Variables include make, model (categorical), mpg (quantitative - mpg), and fuel cost (quantitative - dollars).

Step by step solution

01

Identify the Individuals

The individuals in a data set refer to the entities that are described by the data. For this data set about fuel economy, the individuals are each model year 2016 motor vehicle that the data describes.
02

Examine the Variables

The variables given in this data set might include various aspects like make, model, engine type, miles per gallon (mpg), and annual fuel cost. We would need the full data set to enumerate each variable specifically.
03

Classify Variables as Categorical or Quantitative

Categorical variables describe qualities or characteristics and include data such as make and model, which are strings. Quantitative variables are numerical and can be measured, such as mpg and annual fuel cost.
04

Determine Units for Quantitative Variables

Quantitative variables are often measured in specific units. In this case, 'miles per gallon' (mpg) is measured in miles per gallon, and the annual fuel cost is measured in dollars.

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Key Concepts

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

Individuals in Data
In statistics education, understanding the concept of individuals in data is crucial. Individuals are the distinct entities about which data is collected. In our fuel economy data set example, the individuals are each of the model year 2016 motor vehicles listed. This means every row or entry in the data set corresponds to a particular vehicle, with details about its performance and specifications. When analyzing data, it's essential to identify the individuals to comprehend what the information represents. This insight helps in making informed decisions or analyses based on the data set. Recognizing individuals accurately ensures the relevance and applicability of any findings drawn from the analysis.
Categorical vs Quantitative Variables
When examining data, classifying variables into categorical or quantitative kinds is fundamental. Categorical variables are those that describe attributes or qualities. They often involve types or categories like make or model of a car, which convey distinct groups or classes without a numerical basis.
Quantitative variables, on the other hand, are numerical. They express quantities and are measurable. For example, in the fuel economy data, 'miles per gallon' (mpg) and 'annual fuel cost' are quantitative variables. They involve numbers that can be calculated or subjected to statistical operations.
Understanding the difference between these types of variables helps in choosing the right analytical methods. Categorical data can be summarized through counts or percentages, while quantitative data can be averaged or used in advanced calculations.
Units of Measurement
Correctly identifying the units of measurement for quantitative variables prevents confusion. The unit gives context to numbers, explaining what measurements are in practical terms.
For our fuel economy data, 'miles per gallon' (mpg) is expressed in miles per gallon. This indicates how far a vehicle can travel on a gallon of fuel. Therefore, understanding mpg helps consumers compare fuel efficiency across different vehicles.
The 'annual fuel cost' is usually given in monetary units, like dollars. Knowing this helps in assessing annual fuel expenses, which could influence buying decisions for vehicles based on fuel economy.
By clarifying the units of measurement, we interpret data accurately and effectively, ensuring that all comparisons and analyses are meaningful.

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Most popular questions from this chapter

Child mortality rates. Although child mortality rates have dropped by more than \(50 \%\) since 1990 , in 2015 it was still the case that 16,000 children under five years old died each day. The mortality rates for children under five varied from \(1.9\) per 1000 in Luxembourg to \(156.9\) per 1000 in Angola. Although the data set includes 213 countries, the child mortality rates of 22 country were not available on the World Health Organization database. The data set is too large to print here, but here are the data for the first five countries: \({ }^{27}\) - II MORTALTY (a) Why do you think that mortality rates are measured as the number of deaths per 1000 children under age five rather than simply the number of deaths? (b) Make a histogram that displays the distribution of child mortality rates. Describe the shape, center, and variability of the distribution. Do any countries appear to be obvious outliers in the histogram?

A political party's data bank includes the zip codes of past donors, such as \(\begin{array}{lllllll}47906 & 34236 & 53075 & 10010 & 90210 & 75204 & 30304\end{array}\) Zip code is a (a) quantitative variable. (b) categorical variable.

You look at real estate ads for houses in Naples, Florida. There are many houses ranging from \(\$ 200,000\) to \(\$ 500,000\) in price. The few houses on the water, however, have prices up to \(\$ 15\) million. The distribution of house prices will be (a) skewed to the left. (b) roughly symmetric. (c) skewed to the right.

Buying a refrigerator. Consumer Reports will have an article comparing refrigerators in the next issue. Some of the characteristics to be included in the report are the brand name and model; whether it has a top, bottom, or side-byside freezer; the estimated energy consumption per year (kilowatts); whether or not it is Energy Star compliant; the width, depth, and height in inches; and both the freezer and refrigerator net capacity in cubic feet. Which of these variables are categorical, and which are quantitative? Give the units for the quantitative variables and the categories for the categorical variables. What are the individuals in the report?

Medical students. Students who have finished medical school are assigned to residencies in hospitals to receive further training in a medical specialty. Here is part of a hypothetical database of students seeking residency positions. USMLE is the student's score on Step 1 of the national medical licensing examination. (a) What individuals does this data set describe? (b) In addition to the student's name, how many variables does the data set contain? Which of these variables are categorical, and which are quantitative? If a variable is quantitative, what units is it measured in?
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