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The article “Computing and Using Rural versus Urban
Chapter 1, Problem 15SE(choose chapter or problem)
The article “Computing and Using Rural versus Urban Measures in Statistical Applications” (C. Goodall, K. Kafadar, and J. Tukey, The American Statistician, 1998:101–111) discusses methods to measure the degree to which U.S. counties are urban rather than rural. The following frequency table presents population frequencies of U.S. counties. Populations are on the \(\mathrm {log_2}\) scale; thus the first interval contains counties whose populations are at least \(2^6=64\) but less than \(2^{12.4}=5404\), and so on.
a. Construct a histogram from the frequency table.
b. Estimate the proportion of counties whose populations are greater than 100,000.
c. Is the histogram skewed to the left, skewed to the right, or approximately symmetric?
d. Construct a histogram using the actual populations rather than their logs. Why do you think the article transformed the populations to the log scale?
Equation Transcription:
Text Transcription:
log_2
2^6=64
2^12.4=5404
log_2
Questions & Answers
QUESTION:
The article “Computing and Using Rural versus Urban Measures in Statistical Applications” (C. Goodall, K. Kafadar, and J. Tukey, The American Statistician, 1998:101–111) discusses methods to measure the degree to which U.S. counties are urban rather than rural. The following frequency table presents population frequencies of U.S. counties. Populations are on the \(\mathrm {log_2}\) scale; thus the first interval contains counties whose populations are at least \(2^6=64\) but less than \(2^{12.4}=5404\), and so on.
a. Construct a histogram from the frequency table.
b. Estimate the proportion of counties whose populations are greater than 100,000.
c. Is the histogram skewed to the left, skewed to the right, or approximately symmetric?
d. Construct a histogram using the actual populations rather than their logs. Why do you think the article transformed the populations to the log scale?
Equation Transcription:
Text Transcription:
log_2
2^6=64
2^12.4=5404
log_2
ANSWER: