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# The article “Computing and Using Rural versus Urban

ISBN: 9780073401331 38

## Solution for problem 15SE Chapter 1

Statistics for Engineers and Scientists | 4th Edition

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Problem 15SE

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 log2 scale; thus the first interval contains counties whose populations are at least 26 = 64 but less than 2’14 = 5404. and so on.

 log2 Population Number of Counties 6.0-< 12.4 305 12.4—< 13.1 294 13.1-< 13.6 331 13.6-< 14.0 286 14.0-< 14.4 306 14.4—< 14.8 273 14.8—< 15.3 334 15.3—< 16.0 326 16.0-< 17.0 290 17.0—< 23.0 323

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?

Step-by-Step Solution:

Step 1 of 5:

The given frequency table presents population frequencies of U.S. counties.

 log2 population Number of counties 6.0-12.4 305 12.4-13.1 294 13.1-13.6 331 13.6-14 286 14-14.4 306 14.4-14.8 273 14.8-15.3 334 15.3-16 326 16-17 290 17-23 323

Step 2 of 5:

a).  To construct a histogram from the frequency table.

Step 3 of 5:

b).  0.14 populations are greater than 100000.

Step 4 of 5

Step 5 of 5

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