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a. What percentage of the survey answered "not sure"? b. What percentage think that middle-class is from $25,000 to $50,000? c. Construct a histogram of the data. i. Should all bars have the same width, based on the data? Why or why not? ii. How should the <20,000 and the 100,000+ intervals be handled? Why? d. Find the 40th and 80th percentiles e. Construct a bar graph of the data

a. What percentage of the survey answered "not sure"? b. What percentage think that middle-class is from $25,000 to $50,000? c. Construct a histogram of the data. i. Should all bars have the same width, based on the data? Why or why not? ii. How should the <20,000 and the 100,000+ intervals be handled? Why? d. Find the 40th and 80th percentiles e. Construct a bar graph of the data

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Six hundred adult Americans were asked by telephone poll, "What do you think constitutes a middle-class income?"
The results are in Table 2.71. Also, include left endpoint, but not the right endpoint.
Salary ($) Relative Frequency
< 20,000 0.02
20,000–25,000 0.09
25,000–30,000 0.19
30,000–40,000 0.26
40,000–50,000 0.18
50,000–75,000 0.17
75,000–99,999 0.02
100,000+ 0.01
Table 2.71
a. What percentage of the survey answered "not sure"?
b. What percentage think that middle-class is from $25,000 to $50,000?
c. Construct a histogram of the data.
i. Should all bars have the same width, based on the data? Why or why not?
ii. How should the <20,000 and the 100,000+ intervals be handled? Why?
d. Find the 40th and 80th percentiles
e. Construct a bar graph of the data

### Understanding Middle-Class Income Perceptions In a survey conducted among six hundred adult Americans, participants were asked via telephone, "What do you think constitutes a middle-class income?" The responses are summarized in Table 2.71, which presents income ranges alongside their relative frequencies. #### Table 2.71: Income Ranges and Relative Frequencies | Salary ($) | Relative Frequency | |--------------------|--------------------| | < 20,000 | 0.02 | | 20,000–25,000 | 0.09 | | 25,000–30,000 | 0.19 | | 30,000–40,000 | 0.26 | | 40,000–50,000 | 0.18 | | 50,000–75,000 | 0.17 | | 75,000–99,999 | 0.02 | | 100,000+ | 0.01 | #### Questions and Analysis: a. **Percentage of "Not Sure" Responses**: Determine what percentage of those surveyed did not provide a definitive answer. b. **Middle-Class Income Perception**: Calculate the percentage of participants who identify middle-class incomes as ranging from $25,000 to $50,000. c. **Constructing a Histogram**: Create a histogram to visually represent the data. Consider: i. Should all bars have the same width based on the data? Analyze the appropriateness of bar widths in relation to the data intervals. ii. Discuss how to handle the <20,000 and 100,000+ intervals, explaining any unique treatment of these categories. d. **Finding Percentiles**: Identify the 40th and 80th percentiles of the data. e. **Bar Graph Construction**: Construct a bar graph to illustrate the findings, clearly noting the relative frequencies for each income bracket. This analysis provides insights into public perceptions of what constitutes a middle-class income, highlighting how these views are distributed across different salary ranges.
Transcribed Image Text:### Understanding Middle-Class Income Perceptions In a survey conducted among six hundred adult Americans, participants were asked via telephone, "What do you think constitutes a middle-class income?" The responses are summarized in Table 2.71, which presents income ranges alongside their relative frequencies. #### Table 2.71: Income Ranges and Relative Frequencies | Salary ($) | Relative Frequency | |--------------------|--------------------| | < 20,000 | 0.02 | | 20,000–25,000 | 0.09 | | 25,000–30,000 | 0.19 | | 30,000–40,000 | 0.26 | | 40,000–50,000 | 0.18 | | 50,000–75,000 | 0.17 | | 75,000–99,999 | 0.02 | | 100,000+ | 0.01 | #### Questions and Analysis: a. **Percentage of "Not Sure" Responses**: Determine what percentage of those surveyed did not provide a definitive answer. b. **Middle-Class Income Perception**: Calculate the percentage of participants who identify middle-class incomes as ranging from $25,000 to $50,000. c. **Constructing a Histogram**: Create a histogram to visually represent the data. Consider: i. Should all bars have the same width based on the data? Analyze the appropriateness of bar widths in relation to the data intervals. ii. Discuss how to handle the <20,000 and 100,000+ intervals, explaining any unique treatment of these categories. d. **Finding Percentiles**: Identify the 40th and 80th percentiles of the data. e. **Bar Graph Construction**: Construct a bar graph to illustrate the findings, clearly noting the relative frequencies for each income bracket. This analysis provides insights into public perceptions of what constitutes a middle-class income, highlighting how these views are distributed across different salary ranges.
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