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Ch. 2 - Descriptive Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 2 - Descriptive StatisticsProblem 2.3.14
Chapter 2, Problem 2.3.14

Matching In Exercises 13–16, match the distribution with one of the graphs in Exercises 9–12. Justify your decision.
The frequency distribution of mileages of service vehicles at a business where a few vehicles have much higher mileages than the majority of vehicles

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Identify the key characteristics of the distribution described in the problem. The problem mentions that a few vehicles have much higher mileages than the majority, which suggests the data is skewed to the right (positively skewed).
Review the graphs provided in Exercises 9–12. Look for a graph that shows a right-skewed distribution, where the majority of the data is concentrated on the left side, and the tail extends to the right.
Understand the relationship between the frequency distribution and the graph. A frequency distribution summarizes the data into intervals, and the graph visually represents this distribution. Match the graph that aligns with the description of the data.
Justify your choice by explaining how the shape of the graph corresponds to the description of the data. For example, the presence of a long tail on the right side of the graph aligns with the description of a few vehicles having much higher mileages.
Conclude by confirming that the selected graph accurately represents the frequency distribution of the mileages, based on the characteristics of the data provided in the problem.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Frequency Distribution

A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into categories or intervals, showing the number of observations within each category. This helps in visualizing the data's overall shape and identifying patterns, such as skewness or the presence of outliers.
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Intro to Frequency Distributions

Skewness

Skewness refers to the asymmetry of a probability distribution. A distribution is positively skewed (right-skewed) when a few high values pull the mean to the right, while the majority of values cluster on the left. Understanding skewness is crucial for interpreting data distributions, especially when identifying outliers or making predictions.
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Creating Frequency Polygons

Outliers

Outliers are data points that significantly differ from other observations in a dataset. They can arise from variability in the data or may indicate measurement errors. In the context of the given question, the presence of a few vehicles with much higher mileages suggests that outliers are influencing the overall distribution, which is essential for matching it to the correct graph.
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Comparing Mean vs. Median
Related Practice
Textbook Question

In Exercises 1 and 2, identify the sampling technique used, and discuss potential sources of bias (if any). Explain.

Using random digit dialing, researchers asked 1090 U.S. adults their level of education.

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Textbook Question

Building Basic Skills and Vocabulary


A student’s grade on the Fundamentals of Engineering exam has a z-score of −0.5. Make an observation about the student’s grade.

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Textbook Question

Graphical Analysis In Exercises 21–24, you are asked to compare three data sets.


(c) Estimate the sample standard deviations. Then determine how close each of your estimates is by finding the sample standard deviations.


i. ii. iii.

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Textbook Question

Salary Offers You are applying for jobs at two companies. Company C offers starting salaries with μ = \(59,000 and σ = \)1500. Company D offers starting salaries with μ = \(59,000 and σ = \)1000. From which company are you more likely to get an offer of \$62,000 or more? Explain your reasoning.

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Textbook Question

Constructing Data Sets In Exercises 25–28, construct a data set that has the given statistics.


n = 6

x̄ = 7

s ≈ 2

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Textbook Question

Graphical Analysis In Exercises 19–22, use the box-and-whisker plot to determine whether the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these. Justify your answer.

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