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?

Answer:

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.