Counting National Populations and Areas

Bonnie H. Litwiller and David R. Duncan

Professors of Mathematics, University of Northern Iowa, Cedar Falls, Iowa 50614-0506

Teachers are always seeking situations in which mathematics can be connected to real world data. Data involving the nations of the world can be used as a setting for these connections.

Table I is a listing of the population, area (square kilometres), and 'density' (population ÷ area) for each of the 192 independent nations of the world as listed in The World Almanac and Book of Facts, 1999 (World Almanac Books, publishers).

Table I

Questions for your students based upon the data of Table I.

A. Rank order the 192 nations by population.

1. Find the mean and median of the 192 nations' populations. What does the inequality of these two measures tell about the skewness of the data?

(Mean = 30,776,400; median = 5,807,011, skewed to the right. The median population lies between Honduras and El Salvador.)

2. What is the smallest number of nations needed to account for one-half of the total populations of the nations of Table I?
(Six nations: China, India, United States, Indonesia, Brazil, and Russia.)

3. Fill in the blank with the largest possible number: China has a larger population than the combined total of the ______ smallest nations.
(The sum of the populations of the 162 smallest nations is 1,209,902,866; this is just less than China's population of 1,236,914,658.)

4. Redo problem 3 for the top two counties - China and India.
(The smallest 180 nations are needed.)

B. Rank order the 192 nations by area.

1. Find the mean and median of the 192 nations' areas. What does the inequality of the two measures say about the skewness of data?

(Mean = 694,315; median = 120,929; skewed to the right. The median population lies between Eritrea and North Korea.)

2. What is the smallest number of nations needed to account for one-half of the total area of the nations of Table I; the total area is 133,308,473 square kilometers.
(Eight nations: Russia, Canada, United States, Brazil, Australia, India, and Argentina.)

3. Fill in the blank with the largest possible number: Russia has a larger area than the combined areas of the ______ smallest nations.
(The sum of the areas of the 143 smallest nations is 16,982,938 square kilometers, just less than the area of Russia, which is 17,077,701 square kilometers.)

4. Redo problem 3 for the top two nations in area; these are Russia and Canada.
(158 are needed.)

C. Rank order the 192 nations by density.

1. What is the density of the portion of the world defined by these 192 nations?
(Density )

2. How many of the 192 nations have greater density than that calculated in (1)? (119).

3. Find the total population and area of the seven most densely populated nations: Monaco, Singapore, Vatican City, Malta, Maldives, Bahrain, and Bangladesh.
(This population is 132,376,349 and the area is 145,964 square kilometers.)

4. What is the density of the seven-nation group? (132,376,349 ÷ 145,964 » 907.)

5. If the entire set of nations of Table I were as densely populated as this seven-nation group, what would be the combined nations' population?

. This is approximately 20 times the current population of the entire world.)

6. Suppose that all of China's population were moved to a geographically smaller nation so that the resulting density is 907. In which nation would they 'fit'?

Peru is a nation with approximately that area.)

7. If the entire set of nations of Table I were as densely populated as its seven least densely populated nations, what would be the combined nations' population? The seven least populated nations are: Mongolia, Namibia, Mauritania, Australia, Botswana, Suriname, and Iceland.

(Total population = 27,472,885, total area = 11,955,910 square kilometers. The density is 27,472,885 ÷ 11,955,810 » 2.3. Then = ;

306,322,844. This is just a little more than the population of the United States alone.)

8. Suppose that the entire population of a given nation were moved to a nation with land area that of Russia. Which country should be used so that the resulting population density is 2.3?

This is approximately the population of Spain.)

D. If Scotland were an independent nation:

1. Where would its population rank in Table I?
(The population of Scotland is, according to the almanac, 5,111,000. This would position Scotland as the 106th most populated nation of the new total of 193. In Table I, it would fall between Finland and Georgia.)

2. Where would Scotland's land area of 78,783 square kilometers fall?
(Scotland would rank 114th, between the United Arab Emirates and the Czech Republic.)

3. Where would its population density rank?
(The population density is 64.9. (5,111,000 ÷ 78,783), and ranks 99th, between Boznia-Herzegovina and Malaysia.)

4. If the 192 nations of Table I were as densely populated as Scotland, what would be their total population?

This is nearly 50% larger than the actual population of the nations of Table I. Scotland is more densely populated than the 192 nations as a whole.)

Challenges:

1. Perform the same analysis for the United Kingdom or Scotland and its political subdivisions.

2. Find other situations in which data can be manipulated and characterized.