Textbook Question
IQ Scores IQ scores of adults are normally distributed. If a large sample of adults is randomly selected and the IQ scores are illustrated in a histogram, what is the shape of that histogram?
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Ch. 2 - Exploring Data with Tables and Graphs
Triola14th EditionElementary StatisticsISBN: 9780137366446
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Table of contents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
Chapter 2, Problem 2.3.19
In Exercises 17–20, identify how the graph is deceptive.
Cost of Giving Birth According to the Agency for Healthcare Research and Quality Healthcare Cost and Utilization Project, the typical cost of a C-section baby delivery is \$4500, and the typical cost of a vaginal delivery is \$2600. See the following illustration.
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Examine the illustration provided. The image shows two baby bottles, which might be used to represent the costs of C-section and vaginal deliveries.
Identify the potential deceptive element in the graph. If the bottles are used to visually compare costs, check whether their sizes or proportions accurately reflect the numerical difference between \$4500 and \$2600.
Consider whether the visual representation exaggerates or minimizes the difference between the two costs. For example, if the bottle representing \$4500 is disproportionately larger than the bottle for \$2600, the graph may be misleading.
Analyze whether the graph uses consistent scaling. A deceptive graph might use inconsistent scaling to make the difference appear larger or smaller than it actually is.
Conclude that the graph may be deceptive if it relies on visual elements that do not accurately represent the numerical data, such as disproportionate sizes or misleading scaling.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Graphical Misrepresentation
Graphical misrepresentation occurs when data is presented in a way that distorts the true nature of the information. This can happen through misleading scales, selective data presentation, or inappropriate graph types. In the context of healthcare costs, a graph may exaggerate differences between C-section and vaginal delivery costs, leading to incorrect conclusions about their relative expenses.
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05:54
Intro to Histograms
Cost Comparison
Cost comparison involves evaluating the expenses associated with different options, in this case, C-section versus vaginal delivery. Understanding the typical costs is essential for making informed decisions about healthcare. However, the way these costs are visually represented can influence perceptions, making it crucial to analyze the data critically.
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Contextual Interpretation
Contextual interpretation refers to understanding data within its broader context, including factors that may affect the figures presented. For instance, the costs of childbirth can vary based on location, insurance coverage, and additional medical needs. Recognizing these factors is vital to avoid drawing misleading conclusions from a graph that may not account for all relevant variables.
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Related Practice
Textbook Question
In Exercises 9 and 10, construct the time-series graph.
Home Runs Listed below are the numbers of home runs in Major League Baseball for each year beginning with 1993 (listed in order by row). Is there a trend?
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Textbook Question
In Exercises 9–18, construct the histograms and answer the given questions.
Analysis of Last Digits Use the frequency distribution from Exercise 21 in Section 2-1 to construct a histogram. What can be concluded from the distribution of the digits? Specifically, do the heights appear to be reported or actually measured?
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Textbook Question
In Exercises 5–8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 40 “Coin Weights” in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)
Sample Size What is the approximate number of quarters depicted in the three bars farthest to the left?
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Textbook Question
Boston Commute Time The accompanying table summarizes daily commute times in Boston. How many commute times are included in the summary? Is it possible to identify the exact values of all of the original data amounts?
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Textbook Question
Use Table 2-11 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation?
Using the data from Exercise 6 “Airport Data Speeds,” the linear correlation coefficient is r = 0.866
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