STATEMENT OF PROBLEM

Consider the relationship between the rank and the actual population of cities in a region (world, United States, state, county, etc.) We offer you data on United States cities.

(1-2)*Consider the data on United States cities and plot Population vs. Rank to see if there is any possible relationship.

Population of United States Cities. Source: 1988 World Almanac and Book of Facts. New York: World Almanac. p. 538.

(IF you want current data you will need to consult current Almanac.!)

Rank 1986 Pop City
1 7,262,700 New York
2 3,259,340 Los Angeles
3 3,009,530 Chicago
4 1,728,910 Houston
5 1,642,900 Philadelphia
6 1,086,220 Detroit
7 1,015,190 San Diego
8 1,003,520 Dallas
9 914,350 San Antonio
10 894,070 Phoenix
11 752,800 Baltimore
12 749,000 San Francisco
13 719,820 Indianapolis
20 566,030 Columbus (OH)
30 429,550 Fort Worth

* Considering is HARD WORK and so we give it (1-2) in number!

(3) Conjecture a functional relationship between an independent variable Rank and a dependent variable Population with one or two other parameters to be determined.

(4) Attempt to determine the best parameter(s) for your data and use the value of the parameter value(s) to plot a function relating Population to Rank.

(5) Compare your best parameter model with the actual data.

(6) Consider other demographic data, e.g., countries of the world or cities in your state, and perform the same analysis. Perform the modeling analysis outlined in (1) - (3) above. Be sure to give the full source citation.

You might not want to use all the data offered in your source. In this case use your model which you determine to predict population and rank for cities not used in your analysis. How good is your function? In selected regions of the ranks, e.g., in top ranked and near bottom ranked regions?

(7) Discuss the nature of your models for different types of societies, e.g. a region with a few large industrial centers or a region which is all agrarian. Find data for different types of regions and discuss your model.

(8) An option, find data for one region over time and observe how the parameters in your model change. Attempt to relate your changing parameter to historical phenomena, e.g. war, agrarian reform, industrial revolution, immigration, etc. E.g., United States data from 1790 through 1990.