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In demographics, 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 ways of defining such a "center point", leading to different geographical locations; these are often confused.


Definitions

Three commonly used (but different) center points are: # the ''
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ar ...
center'', also known as the '' centroid'' or ''
center of gravity In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force ma ...
''; # the ''
median In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic f ...
center'', which is the intersection of the median
longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek let ...
and median
latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north ...
; # 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 In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and l ...
.


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 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 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 Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster o ...
(a line of
latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north ...
) and a meridian (a line of
longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek let ...
). In that case, this center is easily found by taking separately the
median In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic f ...
s of the population's latitude and longitude coordinates. John Tukey called this the ''cross median''.


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 In mathematics, a closed-form expression is a mathematical expression that uses a finite number of standard operations. It may contain constants, variables, certain well-known operations (e.g., + − × ÷), and functions (e.g., ''n''th r ...
for the geometric median; it is typically computed using
iterative method In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''n''-th approximation is derived from the pre ...
s.


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
Brasília Brasília (; ) is the federal capital of Brazil and seat of government of the Federal District. The city is located at the top of the Brazilian highlands in the country's Central-West region. It was founded by President Juscelino Kubitsche ...
,
Nur-Sultan Astana, previously known as Akmolinsk, Tselinograd, Akmola, and most recently Nur-Sultan, is the capital city of Kazakhstan. The city lies on the banks of the Ishim River in the north-central part of Kazakhstan, within the Akmola Region, tho ...
or Austin, and, along the same lines, to make tax collection easier. 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 method that does not depend on a two-dimensional projection when dealing with the entire world. In a study from the
Institut national d'études démographiques The French Institute for Demographic Studies (French: ''Institut national d'études démographiques'', INED) is a French research institute specializing in demography and population studies in general. History Before 1945 In 1941, Nobel Prize w ...
, the solution methodology deals only with the globe. As a result, the answer is independent of which
map projection In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and l ...
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 distances as the metric, and a granularity of , 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 where
South Asia South Asia is the southern subregion of Asia, which is defined in both geographical and ethno-cultural terms. The region consists of the countries of Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, and Sri Lanka.;;;;; ...
meets
Central Asia Central Asia, also known as Middle Asia, is a region of Asia that stretches from the Caspian Sea in the west to western China and Mongolia in the east, and from Afghanistan and Iran in the south to Russia in the north. It includes the fo ...
with an average distance of to all humans. The data used in the reference support this result to a precision of only a few hundred kilometers, hence the exact location is not known. Another analysis utilising city level population data found that the world's center of population is located close to
Almaty Almaty (; kk, Алматы; ), formerly known as Alma-Ata ( kk, Алма-Ата), is the largest city in Kazakhstan, with a population of about 2 million. It was the capital of Kazakhstan from 1929 to 1936 as an autonomous republic as part of ...
, Kazakhstan.


By country


Australia

Australia's population centroid is in central
New South Wales ) , nickname = , image_map = New South Wales in Australia.svg , map_caption = Location of New South Wales in AustraliaCoordinates: , subdivision_type = Country , subdivision_name = Australia , established_title = Before federation , es ...
. By 1996 it had moved only a little to the north-west since 1911.


Canada

In Canada, a 1986 study placed the point of minimum aggregate travel just north of
Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the anch ...
in the city of Richmond Hill, and moving westward at a rate of approximately 2 metres per day.


China

China's population centroid has wandered within southern
Henan Henan (; or ; ; alternatively Honan) is a landlocked province of China, in the central part of the country. Henan is often referred to as Zhongyuan or Zhongzhou (), which literally means "central plain" or "midland", although the name is a ...
from 1952 to 2005. Incidentally, the two end point dates are remarkably close to each other. China also plots its economic centroid or center of economy/GDP, which has also wandered, and is generally located at the eastern Henan borders.


Estonia

The center of population of Estonia was on the northwestern shore of Lake Võrtsjärv in 1913 and moved an average of 6 km northwest with every decade until the 1970s. The higher immigration rates during the late Soviet occupation to mostly Tallinn and Northeastern Estonia resulted the center of population moving faster towards north and continuing urbanization has seen it move northwest towards Tallinn since the 1990s. The center of population according to the 2011 census was in
Jüri Jüri is a small borough ( et, alevik) in Harju County, northern Estonia. It is located southeast of the capital Tallinn, by the Tallinn–Tartu road (E263), directly after the intersection with Tallinn Ring Road (nr. 11). Jüri is the admin ...
, just 6 km southeast from the border of Tallinn.


Finland

In Finland, the point of minimum aggregate travel is located in the former municipality of Hauho. It is moving slightly to the south-west-west every year because people are moving out of the peripheral areas of northern and eastern Finland.


Germany

In Germany, the centroid of the population is located in Spangenberg,
Hesse Hesse (, , ) or Hessia (, ; german: Hessen ), officially the State of Hessen (german: links=no, Land Hessen), is a state in Germany. Its capital city is Wiesbaden, and the largest urban area is Frankfurt. Two other major historic cities are ...
, close to Kassel.


Great Britain

The centre of population in Great Britain did not move significantly in the 20th century. In 1901, it was in Rodsley, Derbyshire and in 1911 in Longford. In 1971 it was at Newhall,
Swadlincote Swadlincote is a former mining town in the district of South Derbyshire, England, lying within The National Forest area. It borders the counties of Leicestershire and Staffordshire, south-east of Burton upon Trent and north-west of Ashby-d ...
, South Derbyshire and in 2000, it was in Appleby Parva, Leicestershire. Using the 2011 census the population center can be calculated at Snarestone, Swadlincote.


Ireland

The center of population of the entire
island of Ireland Ireland ( ; ga, Éire ; Ulster-Scots: ) is an island in the North Atlantic Ocean, in north-western Europe. It is separated from Great Britain to its east by the North Channel, the Irish Sea, and St George's Channel. Ireland is the s ...
is located near
Kilcock Kilcock () is a town and townland in the north of County Kildare, Ireland, on the border with County Meath. Its population of 6,093 makes it the ninth largest town in Kildare and 76th largest in Ireland. The town is located 35 km (22  ...
, County Kildare. This is significantly further east than the Geographical centre of Ireland, reflecting the disproportionately large cities of the east of the island (
Belfast Belfast ( , ; from ga, Béal Feirste , meaning 'mouth of the sand-bank ford') is the capital and largest city of Northern Ireland, standing on the banks of the River Lagan on the east coast. It is the 12th-largest city in the United Kingdom ...
and
Dublin Dublin (; , or ) is the capital and largest city of Ireland. On a bay at the mouth of the River Liffey, it is in the province of Leinster, bordered on the south by the Dublin Mountains, a part of the Wicklow Mountains range. At the 2016 ...
). The center of population of the
Republic of Ireland Ireland ( ga, Éire ), also known as the Republic of Ireland (), is a country in north-western Europe consisting of 26 of the 32 counties of the island of Ireland. The capital and largest city is Dublin, on the eastern side of the island. ...
is located southwest of
Edenderry Edenderry (; ) is a town in east County Offaly, Ireland. It is near the borders with Counties Kildare, Meath and Westmeath. The Grand Canal runs along the south of Edenderry, through the Bog of Allen, and there is a short spur to the town ...
,
County Offaly County Offaly (; ga, Contae Uíbh Fhailí) is a Counties of Ireland, county in Republic of Ireland, Ireland. It is part of the Eastern and Midland Region and the Provinces of Ireland, province of Leinster. It is named after the Ancient Ireland ...
.


Japan

The centroid of population of Japan is in
Gifu Prefecture is a prefecture of Japan located in the Chūbu region of Honshu. Gifu Prefecture has a population of 1,991,390 () and has a geographic area of . Gifu Prefecture borders Toyama Prefecture to the north; Ishikawa Prefecture to the northwest, ...
, almost directly north of
Nagoya is the largest city in the Chūbu region, the fourth-most populous city and third most populous urban area in Japan, with a population of 2.3million in 2020. Located on the Pacific coast in central Honshu, it is the capital and the most po ...
city, and has been moving east-southeast for the past few decades. More recently, the only large regions in Japan with significant population growth have been in Greater Nagoya and Greater Tokyo.


New Zealand

In June 2008, New Zealand's median center of population was located near
Taharoa Taharoa ( mi, Tahaaroa or ) is a small village on the west coast of the North Island of New Zealand, to the southwest of Kawhia Harbour and overlooking Lake Taharoa. The New Zealand Ministry for Culture and Heritage gives a translation of "long ...
, around 100 km (65 mi) southwest of
Hamilton Hamilton may refer to: People * Hamilton (name), a common British surname and occasional given name, usually of Scottish origin, including a list of persons with the surname ** The Duke of Hamilton, the premier peer of Scotland ** Lord Hamilto ...
on the North Island's west coast. In 1900 it was near Nelson and has been moving steadily north (towards
Auckland Auckland (pronounced ) ( mi, Tāmaki Makaurau) is a large metropolitan city in the North Island of New Zealand. The most populous urban area in the country and the fifth largest city in Oceania, Auckland has an urban population of about I ...
, the country's most populous city) ever since.


Sweden

The demographical center of Sweden (using the median center definition) is Hjortkvarn in Hallsberg Municipality, Örebro 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.


Russia

The center of population in the Russian Federation is calculated by A. K. Gogolev to be at , south of
Izhevsk Izhevsk (russian: Иже́вск, p=ɪˈʐɛfsk; udm, Ижкар, ''Ižkar'', or , ''Iž'') is the capital city of Udmurtia, Russia. It is situated along the Izh River, west of the Ural Mountains in Eastern Europe. It is the 21st-largest city ...
.


Taiwan

The center of population of Taiwan is located in Heping District, Taichung.


United States

The mean center of the United States population (using the centroid definition) has been calculated for each U.S. Census since 1790. Over the last two centuries, it has progressed westward and, since 1930, southwesterly, reflecting population drift. For example, in 2010, the mean center was located near
Plato, Missouri Plato is an incorporated village in northwestern Texas County, Missouri, United States. It is located approximately 20 miles northwest of Houston and 10 miles south of Fort Leonard Wood on Route 32. The population was 82 at the 2020 census. As ...
, in the south-central part of the state, whereas, in 1790, it was in Kent County, Maryland, east-northeast of the future federal capital, Washington, D.C.


See also

* Extremes on Earth


Sources

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


References

{{reflist, colwidth=30em


External links


Australian parliamentary research paper with map of population centroids


Lists of coordinates Demography
Population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction usi ...