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Chapter 1: Problem 31

For which of the following would it be inappropriate to display the data with a single pie chart? (a) The distribution of car colors for vehicles purchased in the last month. (b) The distribution of unemployment percentages for each of the 50 states. (c) The distribution of favorite sport for a sample of 30 middle school students. (d) The distribution of shoe type worn by shoppers at a local mall. (e) The distribution of presidential candidate preference for voters in a state.

Short Answer

Expert verified
Option (b) is inappropriate for a pie chart because it represents independent data points for each state, not parts of a whole.

Step by step solution

01

Understanding Pie Charts

Pie charts are used to represent proportions of categories within a whole. They are ideal for data where each category forms a part of the total and where the total is 100% or a logical whole.
02

Evaluating Option (a)

The distribution of car colors for vehicles purchased in the last month represents different categories (colors) that sum to the total number of cars purchased. A pie chart is suitable here because each color's share of the cars forms a part of the whole.
03

Evaluating Option (b)

The distribution of unemployment percentages for each of the 50 states does not fit well with pie charts. These percentages do not belong to parts of a single whole but rather are individual data points related to different entities (the states), making a pie chart inappropriate.
04

Evaluating Option (c)

The distribution of favorite sports for a sample of 30 middle school students divides the total sample into categories based on sport preferences, which can all be part of a whole. Thus, a pie chart can be used here.
05

Evaluating Option (d)

The distribution of shoe type worn by shoppers at a local mall describes different categories of shoes that add up to the total number of shoppers. This data fits well in a pie chart.
06

Evaluating Option (e)

The distribution of presidential candidate preference for voters in a state divides voters into categories based on their candidate preference, which represents parts of the total number of voters. A pie chart would be appropriate for this scenario.
07

Identifying the Inappropriate Option

From the evaluation, option (b) is not suitable for a pie chart because it represents multiple separate entities (states), not parts of a single whole.

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Key Concepts

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

Data Representation
Data representation is the way we illustrate information in a visual format to make it easier to understand and interpret. Various graphical methods like pie charts, bar graphs, and line charts are used to show data trends and patterns. Pie charts are a classic way to represent data where each slice signifies a category of the whole. This method is beneficial when you want to compare parts of a whole.
  • Proportions: Pie charts are excellent for illustrating proportions and percentages, giving a quick visual for how categories contribute to a whole.
  • Clarity: They provide clarity with categorical data by allowing instant comparison of different sections.
Choosing the right type of chart is crucial because not every data type is suitable for every chart. For example, pie charts struggle with data not forming a complete whole or when there are many categories with small values.
Categorical Data
Categorical data is information that can be divided into groups or categories. These data types are generally qualitative, and they describe characteristics or attributes such as color, brand, or preference.
  • Types: Categorical data can be nominal, where categories are in no particular order (like car colors), or ordinal, where the order matters (like rating scales).
  • Visualization: Pie charts, bar charts, and histograms are commonly used to represent categorical data.
  • Analysis: Understanding categorical data involves observing trends, differences, or relationships between the categories.
In the provided exercise, each answer choice represents a type of categorical data, showing how it can be divided into distinct groups.
Educational Statistics
Educational statistics involves analyzing data related to educational contexts to derive meaningful insights. This could include anything from student preferences to performance statistics. Data representation forms the backbone of educational statistics because it allows educators to make data-driven decisions effectively.
  • Practices: It often involves collecting data sets, dividing them into comprehensible parts, and choosing the appropriate graphical method.
  • Applications: For example, understanding students' favorite subjects via surveys and visualizing results with pie charts can aid curriculum planning.
The scenario with middle school students' favorite sports illustrates an educational statistics example where categorical data informs decisions or educational strategies.
Graphical Displays
Graphical displays, such as pie charts, are critical for visualizing data effectively. They help highlight patterns, differences, and relationships within data quickly and clearly. Different types of data require different types of graphical displays.
  • Choice of Display: The choice depends on the data type and the insight one hopes to achieve. For instance, pie charts work well for limited categories but might not be suitable for comparisons across many categories or entities.
  • Benefits: They simplify complex data into visual representations, allowing a broader audience to understand the information.
  • Limitations: Avoid using pie charts for data with many small categories or where precise comparison is necessary, as it can result in a cluttered visualization.
Understanding graphical displays allows for using the most effective method for presenting data, ensuring accurate interpretation and communication.

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Most popular questions from this chapter

For each of the following summary statistics, decide (i) whether it could be used to measure center or spread and (ii) whether it is resistant. (a) \(\frac{Q_{1}+Q_{3}}{2}\) (b) \(\frac{\text { Max }-\text { Min }}{2}\)

The following table displays the total number of gold medals won by a sample of countries in the 2012 Summer Olympic Games in London. $$ \begin{array}{lclc} \hline & \text { Gold } & & \text { Gold } \\ \text { Country } & \text { medals } & \text { Country } & \text { medals } \\\ \text { Sri Lanka } & 0 & \text { Thailand } & 0 \\ \text { China } & 38 & \text { Kuwait } & 0 \\ \text { Vietnam } & 0 & \text { Bahamas } & 1 \\ \text { Great Britain } & 29 & \text { Kenya } & 2 \\ \text { Norway } & 2 & \text { Trinidad and Tobago } & 1 \\ \text { Romania } & 2 & \text { Greece } & 0 \\ \text { Switzerland } & 2 & \text { Mozambique } & 0 \\ \text { Armenia } & 0 & \text { (azakhstan } & 7 \\ \text { Netherlands } & 6 & \text { Denmark } & 2 \\ \text { India } & 0 & \text { Latvia } & 1 \\ \text { Georgia } & 1 & \text { Czech Republic } & 4 \\ \text { Kyrgyzstan } & 0 & \text { Hungary } & 8 \\ \text { costa Rica } & 0 & \text { Sweden } & 1 \\ \text { Brazil } & 3 & \text { Uruguay } & 0 \\ \text { Uzbekistan } & 1 & \text { United States } & 46 \\ \hline \end{array} $$ (a) Make a dotplot to display these data. Describe the overall pattern of the distribution and any departures from that pattern. (b) Overall, 205 countries participated in the 2012 Summer Olympics, of which 54 won at least one gold medal. Do you believe that the sample of countries listed in the table is representative of this larger population? Why or why not?

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. (d) unimodal. (e) too high.

The bar graph displays data on students' responses to the question "Which of these methods do you most often use to communicate with your friends?" (a) Would it be appropriate to make a pie chart for these data? Why or why not? (b) Jerry says that he would describe this bar graph as skewed to the right. Explain why Jerry is wrong.

The following bar graph shows the distribution of favorite subject for a sample of 1000 students. What is the most serious problem with the graph? (a) The subjects are not listed in the correct order. (b) This distribution should be displayed with a pie chart. (c) The vertical axis should show the percent of students. (d) The vertical axis should start at 0 rather than 100 . (e) The foreign language bar should be broken up by language.
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