Elderly Populations: Percentages, numbers and totalsDavid R. Duncan and Bonnie H. Litwiller
Professors of Mathematics; University of Northern Iowa, Cedar Falls, Iowa 50614-0506
Teachers are always seeking ways to connect mathematics to other disciplines. One such connection involves mathematics and social studies and ways in which percents can be compared. We shall present an activity that involves the elderly (ages ³ 65) populations in the 185 nations of the world for which this information is available, as listed in The World Almanac and Book of Facts 1999.
Table I lists for each of these nations: its total population, the percent of the population ³ 65 in age, and the approximate number of each nation's population which is ³ 65 in age. The population and percent data were taken from the source cited above; the number of elderly were calculated from these two data entries. [An electronic version of this data can be accessed on the SMC website at www.scot-maths.co.uk]
Table I
Nations | Population | Percent of Population 65 years of age or older | Number of people 65 years of age or older |
| Afghanistan | 24,792,375 | 2.7 | 669,000 |
| Albania | 3,300,754 | 5.9 | 195,000 |
| Algeria | 30,480,793 | 3.8 | 1,158,000 |
| Andorra | 64,716 | 12.3 | 7,960 |
| Angola | 10,864,512 | 2.7 | 293,000 |
| Antigua & Barbuda | 64,006 | 5.6 | 3,580 |
| Argentina | 36,265,463 | 10.2 | 3,699,000 |
| Armenia | 3,421,775 | 8.4 | 287,000 |
| Australia | 18,613,087 | 12.4 | 2,308,000 |
| Austria | 8,133,611 | 15.5 | 1,261,000 |
| Azerbaijan | 7,855,576 | 6.4 | 503,000 |
| Bahamas | 279,833 | 5.5 | 15,400 |
| Bahrain | 616,342 | 2.8 | 17,300 |
| Bangladesh | 127,567,002 | 3.2 | 4,082,000 |
| Barbados | 259,025 | 10.1 | 26,200 |
| Belarus | 10,409,050 | 13.4 | 1,395,000 |
| Belgium | 10,174,922 | 16.8 | 1,709,000 |
| Belize | 230,160 | 3.6 | 8,290 |
| Benin | 6,100,799 | 2.3 | 140,000 |
| Bhutan | 1,908,307 | 3.9 | 74,400 |
| Bolivia | 7,826,352 | 4.5 | 352,000 |
| Bosnia & Herzegovina | 3,365,727 | 11.7 | 394,000 |
| Botswana | 1,448,454 | 3.8 | 55,000 |
| Brazil | 169,806,557 | 5.1 | 8,660,000 |
| Brunei | 315,292 | 4.4 | 13,900 |
| Bulgaria | 8,240,426 | 15.9 | 1,310,000 |
| Burkina Faso | 11,266,393 | 3.0 | 338,000 |
| Burundi | 5,537,387 | 3.0 | 166,000 |
| Cambodia | 11,339,562 | 3.0 | 340,000 |
| Cameroon | 15,029,433 | 3.3 | 496,000 |
| Canada | 30,675,398 | 12.5 | 3,834,000 |
| Cape Verde | 399,857 | 6.1 | 24,400 |
| Central African Republic | 3,375,771 | 3.6 | 122,000 |
| Chad | 7,359,512 | 3.0 | 221,000 |
| Chile | 14,787,781 | 7.0 | 1,035,000 |
| China | 1,236,914,658 | 6.6 | 81,636,000 |
| Colombia | 38,580,949 | 4.5 | 1,736,000 |
| Comoros | 545,528 | 2.8 | 15,300 |
| Congo | 49,000,511 | 2.6 | 1,274,000 |
| Congo Republic | 2,658,123 | 3.4 | 90,400 |
| Costa Rica | 3,604,642 | 5.0 | 180,000 |
| Cote D'Ivoire | 15,446,231 | 2.2 | 340,000 |
| Croatia | 4,671,584 | 14.7 | 687,000 |
| Cuba | 11,050,729 | 9.5 | 1,050,000 |
| Cyprus | 748,982 | 10.4 | 77,900 |
| Czech Republic | 10,286,470 | 13.7 | 1,409,000 |
| Denmark | 5,333,617 | 14.9 | 795,000 |
| Djibouti | 440,727 | 2.6 | 11,500 |
| Dominica | 65,777 | 9.5 | 6,250 |
| Dominican Republic | 7,998,766 | 4.4 | 352,000 |
| Ecuador | 12,336,572 | 4.4 | 543,000 |
| Egypt | 66,050,004 | 3.7 | 2,444,000 |
| El Salvador | 5,752,067 | 5.2 | 299,000 |
| Equatorial Guinea | 454,001 | 3.8 | 17,300 |
| Eritrea | 3,842,436 | 3.3 | 127,000 |
| Estonia | 1,421,335 | 14.3 | 203,000 |
| Ethiopia | 58,390,351 | 2.8 | 1,635,000 |
| Fiji | 802,611 | 3.2 | 25,700 |
| Finland | 5,149,242 | 14.6 | 752,000 |
| France | 58,804,944 | 15.8 | 9,291,000 |
| Gabon | 1,207,844 | 5.5 | 66,400 |
| The Gambia | 1,291,858 | 2.7 | 34,900 |
| Georgia | 5,108,527 | 12.1 | 618,000 |
| Germany | 82,079,454 | 15.9 | 13,051,000 |
| Ghana | 18,497,206 | 3.1 | 573,000 |
| Greece | 10,662,138 | 16.5 | 1,759,000 |
| Grenada | 96,217 | 4.6 | 4,430 |
| Guatemala | 12,007,580 | 3.5 | 420,000 |
| Guinea | 7,447,110 | 2.7 | 201,000 |
| Guinea-Bissau | 1,206,311 | 2.8 | 33,800 |
| Guyana | 707,954 | 4.6 | 32,600 |
| Haiti | 6,780,501 | 4.1 | 278,000 |
| Honduras | 5,861,955 | 3.4 | 199,000 |
| Hungary | 10,208,127 | 14.4 | 1,470,000 |
| Iceland | 271,033 | 11.7 | 31,700 |
| India | 984,003,683 | 4.6 | 45,264,000 |
| Indonesia | 212,941,810 | 4.0 | 8,518,000 |
| Iran | 68,959,931 | 4.1 | 2,827,000 |
| Iraq | 21,722,287 | 3.2 | 695,000 |
| Ireland | 3,619,480 | 11.3 | 409,000 |
| Israel | 5,643,966 | 9.9 | 559,000 |
| Italy | 56,782,748 | 17.6 | 9,994,000 |
| Jamaica | 2,634,678 | 6.8 | 179,000 |
| Japan | 125,931,533 | 16.0 | 20,149,000 |
| Jordan | 4,434,978 | 2.9 | 129,000 |
| Kazakhstan | 16,846,808 | 7.0 | 1,179,000 |
| Kenya | 28,337,071 | 2.7 | 765,000 |
| North Korea | 21,234,387 | 6.0 | 1,274,000 |
| South Korea | 46,416,796 | 6.4 | 2,971,000 |
| Kuwait | 1,913,285 | 2.0 | 38,300 |
| Kyrgyzstan | 4,522,281 | 6.2 | 280,000 |
| Laos | 5,260,842 | 3.2 | 168,000 |
| Latvia | 2,385,396 | 14.9 | 355,000 |
| Lebanon | 3,505,794 | 6.4 | 224,000 |
| Lesotho | 2,089,829 | 4.6 | 96,100 |
| Liberia | 2,771,901 | 3.5 | 97,000 |
| Libya | 5,690,727 | 2.9 | 165,000 |
| Liechtenstein | 31,717 | 11.0 | 3,490 |
| Lithuania | 3,600,158 | 13.0 | 468,000 |
| Luxembourg | 425,017 | 14.8 | 62,900 |
| Macedonia | 2,009,387 | 9.4 | 189,000 |
| Madagascar | 14,462,509 | 3.3 | 477,000 |
| Malawi | 9,840,474 | 2.7 | 266,000 |
| Malaysia | 20,932,901 | 3.9 | 816,000 |
| Maldives | 290,211 | 3.1 | 9,000 |
| Mali | 10,108,569 | 3.2 | 323,000 |
| Malta | 379,563 | 11.6 | 44,000 |
| Marshall Islands | 63,031 | 2.3 | 1,450 |
| Mauritania | 2,511,473 | 2.4 | 60,300 |
| Mauritius | 1,168,256 | 5.9 | 68,900 |
| Mexico | 98,552,776 | 4.1 | 4,041,000 |
| Moldova | 4,457,729 | 9.7 | 432,000 |
| Monaco | 32,035 | 19.5 | 6,250 |
| Mongolia | 2,578,530 | 3.7 | 95,400 |
| Morocco | 29,114,497 | 4.5 | 1,310,000 |
| Mozambique | 18,641,469 | 2.3 | 429,000 |
| Myanmar | 47,305,319 | 4.2 | 1,987,000 |
| Namibia | 1,622,328 | 4.0 | 64,900 |
| Nepal | 23,698,421 | 4.0 | 948,000 |
| Netherlands | 15,731,112 | 13.5 | 2,124,000 |
| New Zealand | 3,625,388 | 11.6 | 421,000 |
| Nicaragua | 4,583,379 | 2.7 | 124,000 |
| Niger | 9,671,848 | 2.3 | 222,000 |
| Nigeria | 110,532,242 | 2.9 | 3,205,000 |
| Norway | 4,419,955 | 15.7 | 694,000 |
| Oman | 2,363,591 | 2.3 | 54,400 |
| Pakistan | 135,135,195 | 4.0 | 5,405,000 |
| Panama | 2,735,943 | 4.9 | 134,000 |
| Papua New Guinea | 4,599,785 | 3.0 | 138,000 |
| Paraguay | 5,291,020 | 4.6 | 243,000 |
| Peru | 26,111,110 | 4.5 | 1,175,000 |
| Philippines | 77,725,862 | 3.6 | 2,798,000 |
| Poland | 38,606,922 | 11.8 | 4,556,000 |
| Portugal | 9,927,556 | 15.1 | 1,499,000 |
| Qatar | 697,126 | 2.0 | 13,900 |
| Romania | 22,395,848 | 13.0 | 2,911,000 |
| Russia | 146,861,022 | 12.5 | 18,358,000 |
| Rwanda | 7,956,172 | 2.8 | 223,000 |
| Saint Kitts & Nevis | 42,291 | 6.2 | 2,620 |
| Saint Lucia | 152,335 | 5.4 | 8,230 |
| Samoa | 224,713 | 4.1 | 9,210 |
| San Marino | 24,894 | 16.6 | 4,130 |
| Sao Tome & Principe | 150,123 | 4.1 | 6,160 |
| Saudi Arabia | 20,785,955 | 2.4 | 499,000 |
| Senegal | 9,723,149 | 2.8 | 272,000 |
| Seychelles | 78,641 | 6.3 | 4,950 |
| Sierra Leone | 5,080,004 | 3.1 | 157,000 |
| Singapore | 3,490,356 | 6.8 | 237,000 |
| Slovakia | 5,392,982 | 11.3 | 609,000 |
| Slovenia | 1,971,739 | 13.4 | 264,000 |
| Solomon Islands | 441,039 | 3.0 | 13,200 |
| Somalia | 6,841,695 | 2.9 | 198,000 |
| South Africa | 42,834,520 | 4.5 | 1,928,000 |
| Spain | 39,133,996 | 16.3 | 6,379,000 |
| Sri Lanka | 18,933,558 | 6.3 | 1,193,000 |
| Sudan | 33,550,552 | 2.2 | 738,000 |
| Suriname | 427,980 | 5.2 | 22,300 |
| Swaziland | 966,462 | 2.5 | 24,200 |
| Sweden | 8,886,738 | 17.4 | 1,546,000 |
| Switzerland | 7,260,357 | 14.9 | 1,082,000 |
| Syria | 16,673,282 | 2.9 | 484,000 |
| Taiwan | 21,908,135 | 8.2 | 1,796,000 |
| Tajikistan | 6.020,095 | 4.6 | 277,000 |
| Tanzania | 30,608,769 | 2.9 | 888,000 |
| Thailand | 60,037,366 | 6.0 | 3,602,000 |
| Togo | 4,905,827 | 2.2 | 108,000 |
| Trinidad & Tobago | 1,116,595 | 7.3 | 81,500 |
| Tunisia | 9,380,404 | 5.8 | 544,000 |
| Turkey | 64,566,511 | 5.7 | 3,680,000 |
| Turkmenistan | 4,297,629 | 4.2 | 181,000 |
| Tuvalu | 10,444 | 4.7 | 491 |
| Uganda | 22,167,195 | 2.2 | 488,000 |
| Ukraine | 50,125,108 | 14.0 | 7,018,000 |
| United Arab Emirates | 2,303,088 | 1.9 | 43,800 |
| United Kingdom | 58,970,119 | 15.7 | 9,258,000 |
| United States of America | 270,311,758 | 12.7 | 34,330,000 |
| Uruguay | 3,284,841 | 12.9 | 424,000 |
| Uzbekistan | 23,784,321 | 4.7 | 1,118,000 |
| Vanuatu | 185,204 | 3.0 | 5,560 |
| Venezuela | 22,803,409 | 4.5 | 1,026,000 |
| Vietnam | 76,236,259 | 5.3 | 4,041,000 |
| Yemen | 16,387,963 | 3.3 | 541,000 |
| Yugoslavia | 11,206,039 | 11.7 | 1,311,000 |
| Zambia | 9,460,736 | 2.5 | 237,000 |
| Zimbabwe | 11,044,147 | 2.6 | 287,000 |
| 5,908,597,662 | 398,687,251 |
Afghanistan, for example, has a total population of 24,792,375. Of this population, 2.7% is aged 65 or above; the resulting number of elderly persons is 2.7% of 24,792,375 or approximately 669,000.
Questions for the reader and his/her students.
1. What percent of the population of these 185 nations is ³ 65?
2. Rank order Table I by the percent column.
A. List the top 12 nations in terms of the percent of elderly. They are:
| 1. | Monaco | 7. | Spain |
| 2. | Italy | 8. | Japan |
| 3. | Sweden | 9. | Germany and Bulgaria |
| 4. | Belgium | 11. | France |
| 5. | San Marino | 12. | Norway and United Kingdom |
| 6. | Greece |
B. Locate these nations on a world map. What might account for the high percents of elderly?
C. Locate the bottom 12 nations in terms of percent of elderly. These are listed from 'bottom' up.
1. United Arab Emirates
2. Kuwait and Qatar
4. Sudan, Togo, Uganda, Cote d'Ivorie
8. Marshall Islands, Benin, Mozambique, Niger, Oman
D. Locate these nations on a world map. What might account for the low percent of elderly?
E. How many of these 185 nations have a percent of elderly larger than that of the percent for the 185 nations taken as a whole (6.7%)? (Only 61 nations.)
F. Locate these 61 nations on a map. What common characteristics do they appear to share?
G. Which nations are nearest the world-wide percent of 6.7? (These are Jamaica, Singapore, and China.)
3. Rank order Table I in terms of the numbers of elderly
A. List the top 12 nations in terms of numbers of elderly. These are:
| 1. | China | 7. | Italy |
| 2. | India | 8. | France |
| 3. | United States | 9. | United Kingdom |
| 4. | Japan | 10. | Brazil |
| 5. | Russia | 11. | Indonesia |
| 6. | Germany | 12. | Ukraine |
Note the presence of several nations with relatively low elderly percents but high actual numbers of elderly. For instance, the percent of elderly in Indonesia is only 4.0%; but, this small percent applied to a large population of 212,941,810 still yields a relatively large elderly population of 8,518,000.
B. For several nations, their percent rank and their elderly population rank differ by 50 or more positions. Indonesia is one such nation. The percent of elderly (4.0%) ranks 111th, while the number of elderly (8,578,000) ranks 11th. Latvia ranks 16th in percent of elderly (14.9%), but the number of elderly is 90th in rank (355,000). Find other such examples of this disparity and explain mathematically how this can happen.
C. Find pairs of nations which are approximately equal in percent of elderly, but differ widely in number of elderly ranks. For example, Georgia (12.1%) and Poland (11.8%) are adjacent on the table as ranked by percent. However, Poland's number of elderly (4,556,000) ranks 15th and Georgia's number of elderly (618,000) ranks 69th.
Malawi and Slovenia have adjacent ranks in the number of elderly ordering, 266,000 and 264,000 respectively, but the percent ranks are: Malawi - 160th and Slovenia - 27th. Find other such pairs.
D. Fill in the blank: The number of elderly in China is approximately equal to the total population of the smallest nations of Table I. (The population of the 65 smallest nations is 81,648,314. This is approximately the population of China's 65+ population.)
4. Assume the world as a whole (as listed in Table I) had the same percent of elderly as does Italy (17.6%).
A. What would be the new population of the world?
B. What is the number of elderly in the new population?
Let 
= the additional number of elderly. Then,
This is the additional number of elderly. The world's population would then be approximately 6,718,000,000 while the elderly population would grow to approximately 1,200,000,000. The elderly population approximately triples while the world's population increases by about 6%.
Challenges:
1. Find other ways in which to compare and contrast the data of Table I.
2. Find other statistical situations in which data can be manipulated and characterised.