In demographics Demographics or demographic data are the characteristics of a human population as used in government, marketing or opinion research, or the demographic profiles used in such research. Note the distinction from the term "demography" Commonly used demographics include sex, race, age, income, disabilities, mobility (in terms of travel time, the center of population (or population center) of a region is a geographical point that describes a centerpoint of the region's population. There are several different ways of defining such a "center point", leading to different geographical locations; these are often confused.^[1]

Definitions

Three commonly used (but different) center points are:

1. the mean There are other statistical measures that use samples that some people confuse with averages - including 'median' and 'mode'. Other simple statistical analyses use measures of spread, such as range, interquartile range, or standard deviation. For a real-valued random variable X, the mean is the expectation of X. Note that not every probability center, also known as the centroid In geometry, the centroid, geometric center, or barycenter of a plane figure or two-dimensional shape X is the intersection of all straight lines that divide X into two parts of equal moment about the line. Informally, it is the "average" of all points of X. The definition extends to any object X in n-dimensional space: its centroid is or center of gravity The center of mass or mass center is the mean location of all the mass in a system. In the case of a rigid body, the position of the center of mass is fixed in relation to the body. In the case of a loose distribution of masses in free space, such as shot from a shotgun or the planets of the solar system, the position of the center of mass is a;
2. the median In probability theory and statistics, a median is described as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is center, which is the intersection of the median longitude Longitude , identified by the Greek letter lambda (λ), is the geographic coordinate most commonly used in cartography and global navigation for east-west measurement. Constant longitude is represented by lines running from north to south. The line of longitude (meridian) that passes through the Royal Observatory, Greenwich, in England, and median latitude Latitude, usually denoted by the Greek letter phi gives the location of a place on Earth (or other planetary body) north or south of the equator. Lines of Latitude are the imaginary horizontal lines shown running east-to-west (or west to east) on maps (particularly so in the Mercator projection) that run either north or south of the equator;
3. the geometric median, also known as Weber point, Fermat–Weber point, or point of minimum aggregate travel.

A further complication is caused by the curved shape of the Earth. Different center points are obtained depending on whether the center is computed in three-dimensional space, or restricted to the curved surface, or computed using a flat map projection A map projection is any method of representing the surface of a sphere or other shape on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore different map projections exist in order to.

Mean center

The mean center, or centroid, is the point on which a rigid, weightless map would balance perfectly, if the population members are represented as points of equal mass.

Mathematically, the centroid is the point to which the population has the smallest possible sum of squared distances. It is easily found by taking the arithmetic mean There are other statistical measures that use samples that some people confuse with averages - including 'median' and 'mode'. Other simple statistical analyses use measures of spread, such as range, interquartile range, or standard deviation. For a real-valued random variable X, the mean is the expectation of X. Note that not every probability of each coordinate. If defined in the three-dimensional space, the centroid of points on the Earth's surface is actually inside the Earth. This point could then be projected back to the surface. Alternatively, one could define the centroid directly on a flat map projection; this is, for example, the definition that the US Census Bureau The United States Census Bureau is the government agency that is responsible for the United States Census. It also gathers other national demographic and economic data. As part of the United States Department of Commerce, the Census Bureau serves as a leading source of data about America's people and economy uses.

Contrary to a common misconception, the centroid does not minimize the average distance to the population. That property belongs to the geometric median.

Median center

The median center is the intersection of two perpendicular lines, each of which divides the population into two equal halves. Typically these two lines are chosen to be a parallel A circle of latitude, on the Earth, is an imaginary east-west circle connecting all locations that share a given latitude. A location's position along a circle of latitude is given by its longitude (a line of latitude Latitude, usually denoted by the Greek letter phi gives the location of a place on Earth (or other planetary body) north or south of the equator. Lines of Latitude are the imaginary horizontal lines shown running east-to-west (or west to east) on maps (particularly so in the Mercator projection) that run either north or south of the equator) and a meridian A meridian is an imaginary arc on the Earth's surface from the North Pole to the South Pole that connects all locations running along it with a given longitude. The position of a point on the meridian is given by the latitude. Each meridian is perpendicular to all circles of latitude at the intersection points. Each is also the same size, being (a line of longitude Longitude , identified by the Greek letter lambda (λ), is the geographic coordinate most commonly used in cartography and global navigation for east-west measurement. Constant longitude is represented by lines running from north to south. The line of longitude (meridian) that passes through the Royal Observatory, Greenwich, in England,). In that case, this center is easily found by taking separately the medians In probability theory and statistics, a median is described as the numeric value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is of the population's latitude and longitude coordinates.

Geometric median

The geometric median is the point to which the population has the smallest possible sum of distances (or equivalently, the smallest average distance). Because of this property, it is also known as the point of minimum aggregate travel. Unfortunately, there is no direct closed-form expression for the geometric median; it is typically computed using iterative methods In computational mathematics, an iterative method attempts to solve a problem by finding successive approximations to the solution starting from an initial guess. This approach is in contrast to direct methods, which attempt to solve the problem by a finite sequence of operations, and, in the absence of rounding errors, would deliver an exact.

Determination

In practical computation, decisions are also made on the granularity (coarseness) of the population data, depending on population density patterns or other factors. For instance, the center of population of all the cities in a country may be different from the center of population of all the states (or provinces, or other subdivisions) in the same country. Different methods may yield different results.

Practical uses for finding the center of population include locating possible sites for forward capitals, such as Brasilia Brasília is the capital of Brazil. The name is commonly spelled Brasilia in English. The city and its District are located in the Central-West region of the country, along a plateau known as Planalto Central. It has a population of about 2,557,000 (3,599,000 in the metropolitan area) as of the 2008 IBGE estimate, making it the fourth largest city, Astana Astana , formerly known as Akmola (Kazakh: Ақмола / Aqmola, until 1998), Tselinograd (Russian: Целиноград, until 1992) and Akmolinsk (Russian: Акмолинск, until 1961), is the capital and second largest city (after Almaty) of Kazakhstan, with an officially estimated population of 691,529 as of 1 March 2010. It is located in or Austin Austin is the capital of the U.S. state of Texas and the seat of Travis County. Located in Central Texas on the eastern edge of the American Southwest, it is the fourth-largest city in Texas and the 15th-largest in the United States. It was the third-fastest-growing large city in the nation from 2000 to 2006. According to the 2008 U.S. Census. Practical selection of a new site for a capital is a complex problem that depends also on population density patterns and transportation networks.

World

It is important to use a culturally neutral method when dealing with the entire world. As described in INED (Institut national d'études démographiques),^[2] the solution methodology deals only with the globe, and not with a two-dimensional projection of the Earth's surface. As a result, the answer is independent of which map projection A map projection is any method of representing the surface of a sphere or other shape on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore different map projections exist in order to is used or where it is centered. As described above, the exact location of the center of population will depend on both the granularity of the population data used, and the distance metric. With geodesic In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. In the presence of an affine connection, geodesics are defined to be curves whose tangent vectors remain parallel distances as the metric, and a granularity of 1,000 kilometers (600 mi), meaning that two population centers within 1000 km of each other are treated as part of a larger common population center of intermediate location, the world's center of population is found to lie "at the crossroads between China China is seen variously as an ancient civilization extending over a large area in East Asia, a nation and/or a multinational entity, India India, officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with 1.18 billion people, and the most populous democracy in the world. Mainland India is bounded by the Indian Ocean on the south, the Arabian Sea on the west, and the Bay of Bengal on the, Pakistan Pakistan (Urdu pronunciation: [paːkɪsˈtaːn] ( listen)), officially the Islamic Republic of Pakistan (Urdu: اسلامی جمہوریہ پاکِستان), is a country in South Asia. It has a 1,046-kilometre (650 mi) coastline along the Arabian Sea and Gulf of Oman in the south, is bordered by Afghanistan and Iran in the west, and India in the and Tajikistan Tajikistan , officially the Republic of Tajikistan (Tajik: Ҷумҳурии Тоҷикистон, Jumhurii Tojikiston; Russian: Республика Таджикистан, Respublika Tadzhikistan; Persian: جمهوری تاجیکستان Jomhuri-ye Tajikestan), is a mountainous landlocked country in Central Asia. Afghanistan borders it to the", essentially located in Afghanistan The Islamic Republic of Afghanistan is a landlocked country in south-central Asia. It is bordered by Pakistan in the south and east, Iran in the west, Turkmenistan, Uzbekistan and Tajikistan in the north, and China in the far northeast. In addition; India claims a border with Afghanistan at the Wakhan corridor as part of its claim on the Gilgit-, with an average distance of 5,200 kilometers (3,200 mi) to all humans [1]. The data used in the reference support this result to only a precision In the fields of engineering, industry and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to its actual value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results of a few hundred kilometers, hence the exact location is not known.

By country

Australia

Australia For at least 40,000 years before European settlement in the late 18th century, Australia was inhabited by indigenous Australians, who belonged to one or more of the roughly 250 language groups. After sporadic visits by fishermen from the immediate north and discovery by Dutch explorers in 1606, Australia's eastern half was claimed by the British has not seen its population centroid move drastically since the creation of the country. In 1911, the centroid was in central New South Wales New South Wales , Australia's most populous state, is located in the south-east of the country, north of Victoria, south of Queensland, east of South Australia and encompasses the whole of the Australian Capital Territory. It was founded in 1788 and originally comprised much of the Australian mainland, as well as Van Diemen's Land, Lord Howe; in 1996, it was only slightly farther northwest.^[3]

Finland

In Finland Finland (pronounced /ˈfɪnlənd/ ), officially the Republic of Finland Finnish: Suomi; Swedish: Finland (help·info), is a Nordic country situated in the Fennoscandian region of Northern Europe. It is bordered by Sweden on the west, Norway on the north and Russia on the east, while Estonia lies to its south across the Gulf of Finland, the point of minimum aggregate travel is located in the municipality of Hauho.^[4] It is moving slightly to the west and south every year because people are moving out of the periphery areas of northern and eastern Finland.

Germany

In Germany, the centroid of the population is located in Spangenberg The town is known best of all for its Schloss Spangenberg, a castle built in 1253 and the town's landmark. Also worth seeing are the half-timbered buildings in the Old Town and the remains of the town's old wall, several of whose towers are still standing, Hesse Hesse or Hessia (German: Hessen [ˈhɛsən], Hessisch: Hesse [ˈhɛzɛ]) is a state of Germany with an area of 21,110 km2 (8,150 sq mi) and just over six million inhabitants. The state capital is Wiesbaden. Hesse's largest city is nearby Frankfurt am Main close to Kassel Kassel is a town located on the Fulda in northern Hesse, Germany, one of the two origins of the Weser river. It is the administrative seat of the Kassel administrative region (Regierungsbezirk) and of the district (Kreis) of the same name. In 2007 the town had approximately 198,500 inhabitants and has a total area of 107 square kilometers (41.^[5]

Great Britain

The centre of population in Great Britain Great Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island. With a population of about 61.8 million people in mid-2009, it is the third most populated island on Earth. Great Britain is surrounded by over 1,000 smaller islands and islets. The island of did not move much in the 20th century. In 1901, it was in Rodsley Nearby Hollington and Rodsley are included as manors in the 1086 Domesday Survey as belonging to Henry de Ferrers, who was given a large number of manors in Derbyshire. His descendants became the Earls of Derby and still owned land in Shirley in the nineteenth century. Mention is also made of the abbey of Burton as having an interest, Derbyshire 1. High Peak 2. Derbyshire Dales 3. South Derbyshire 4. Erewash 5. Amber Valley 6. North East Derbyshire 7. Chesterfield 8. Bolsover 9. Derby and in 1911 in Longford. In 1971 it was at Newhall, South Derbyshire and in 2000, it was in Appleby Parva, Leicestershire County Hall, situated in Glenfield, about 3 miles north-west of Leicester city centre, is the seat of Leicestershire County Council and the headquarters of the county authority. The City of Leicester is administered from offices in Leicester itself and the City Council meets at Leicester Town Hall.^{[6][7][8][Need quotation to verify]}

Japan

The centroid of population of Japan Japan is an island country in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south. The characters that make up Japan's name mean "sun-origin", which is why Japan is is in Gifu Prefecture Gifu Prefecture is a prefecture located in the Chūbu region of central Japan. Its capital is the city of Gifu. Located in the center of Japan, it has long played an important part as the crossroads of Japan, connecting the east to the west through such routes as the Nakasendō. During the Sengoku period, many people referred to Gifu by saying, &, almost directly north of Nagoya Nagoya is the third-largest incorporated city and the fourth most populous urban area in Japan city, and has been moving East South East for the past few decades.^[9] More recently, the only large regions in Japan with significant population growth have been in Greater Nagoya and Greater Tokyo.

Sweden

The demographical center of Sweden (using the median center definition) is Hjortkvarn in Hallsberg Municipality, Örebro Örebro [œrəˈbruː] is a city, the seat of Örebro Municipality and the capital of Örebro County in Sweden with circa 130.000 inhabitants in 2009 county. Between the 1989 and 2007 census the point moved a few kilometres to the south, due to a decreasing population in northern Sweden and immigration to the south.^[10]

United States

The mean center of United States population During the 20th century the mean center of population has shifted 324 miles west and 101 miles (163 km) south. The southerly movement was much stronger during the second half of the century; 79 miles (127 km) of the 101 miles (163 km) happened between 1950 and 2000 (using the centroid definition) has been calculated for each U.S. Census The United States Census is a decennial census mandated by the United States Constitution. The population is enumerated every 10 years and the results are used to allocate Congressional seats , electoral votes, and government program funding. Some states or local jurisdictions also conduct local censuses since 1790. Currently this point is located in Phelps County Phelps County is a county located in South Central Missouri in the United States. According to the U.S. Census Bureau, it includes the mean center of U.S. population in 2000. As of the 2000 U.S. Census, the county's population was 39,825. A 2008 estimate, however, showed the population to be 42,205. The largest city and county seat is Rolla. The, Missouri Missouri mirrors the demographic, economic and political makeup of the nation with a mix of urban and rural culture. It has long been considered a political bellwether state. With the exceptions of 1956 and 2008, Missouri's results in U.S. presidential elections have accurately predicted the next President of the United States in every election, in the east-central part of the state. However, when Washington, D.C. Washington, D.C. , formally the District of Columbia and commonly referred to as Washington, the District, or simply D.C., is the capital of the United States, founded on July 16, 1790. The City of Washington was originally a separate municipality within the Territory of Columbia until an act of Congress in 1871 effectively merged the City and the was chosen as the federal capital of the United States in 1790, the center of the U.S. population was in Kent County, Maryland Kent County is a county located in the U.S. state of Maryland, on its Eastern Shore. It was named for the county of Kent in England. Its county seat is Chestertown. In 2000, the county population was 19,197. It is the least populous of Maryland's 23 counties, a mere 47 miles (76 km) east-northeast of the new capital. Over the last two centuries, the mean center of United States population has progressed westward and, since 1930, southwesterly, reflecting population drift.

Sources

• Bellone F. and Cunningham R. (1993). "All Roads Lead to... Laxton, Digby and Longford." Statistics Canada 1991 Census Short Articles Series.

References

1. ^ Kumler, Mark P.; Goodchild, Michael F. (1992). "The population center of Canada — Just north of Toronto?!?". in Janelle, Donald G.. Geographical snapshots of North America: commemorating the 27th Congress of the International Geographical Union and Assembly. pp. 275–279.
2. ^ Ined.fr (French)
3. ^ "Figure 15: Shifts in the Australian Population Centroid*, 1911-1996". Parliament of Australia The Parliament of Australia, also known as the Commonwealth Parliament or Federal Parliament, is the legislative branch of the government of Australia. It is bicameral, largely modelled in the Westminster tradition, but with some influences from the United States Congress. According to Section 1 of the Constitution of Australia, Parliament Parliamentary Library. http://www.aph.gov.au/library/pubs/rp/1999-2000/2000rp09.htm#Figure15. Retrieved 2009-01-07.
4. ^ Uusirauma.fi Kaupunkilehti Uusi Rauma 03.08.2009 Päivän kysymys? Missä Rauman keskipiste? (Finnish)
5. ^ Dradio.de (German)
6. ^ "News Item:". University of Leeds The University of Leeds is a British 'Redbrick' university located in the city of Leeds, West Yorkshire, England. The Yorkshire College, a successor to the Leeds School of Medicine, became part of the Victoria University alongside Owens College, which eventually became the University of Manchester, and University College Liverpool, which became. http://reporter.leeds.ac.uk/477/news.htm. Retrieved 2007-11-25.
7. ^ "Population Centre". Appleby Magna & Appleby Parva. http://www.applebymagna.org.uk/population_centre.htm. Retrieved 2007-11-25.
8. ^ "Coffee Break: The movable Midlands; ANSWERS TO CORRESPONDENTS". The Daily Mail: pp. 64. 7 February 2002.
9. ^ Our Country's Center of Population (我が国の人口重心)
10. ^ Sweden's demographic centre, SCB.se, 2008-03-18

External links

• Australian parliamentary research paper with map of population centroids.
• Population centers of each U.S. state, 2000 (United States Census Bureau The United States Census Bureau is the government agency that is responsible for the United States Census. It also gathers other national demographic and economic data. As part of the United States Department of Commerce, the Census Bureau serves as a leading source of data about America's people and economy)

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