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. [1]
Three commonly used (but different) center points are:
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.
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.
The median center is the intersection of two perpendicular lines, each of which divides the population into two equal halves. [2] Typically these two lines are chosen to be a parallel (a line of latitude) and a meridian (a line of longitude). In that case, this center is easily found by taking separately the medians of the population's latitude and longitude coordinates. John Tukey called this the cross median. [3]
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.[ citation needed ]
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, Astana 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.
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, [4] the solution methodology deals only with the globe. As a result, the answer is independent of which map projection 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 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, India, Pakistan and Tajikistan" with an average distance of 5,200 kilometers (3,200 mi) to all humans. [4] 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, using city-level population data, found that the world's center of population is close to Almaty, Kazakhstan. [5]
Australia's population centroid is in central New South Wales. By 1996, it had moved only a little to the north-west since 1911. [6] It moved only 1.4 km north in 2022 from the previous year [7] and in 2023 moved 1.9 km west compared to 2022, located 40 km east of Ivanhoe. [8]
In Canada, a 1986 study placed the point of minimum aggregate travel just north of Toronto in the city of Richmond Hill, and moving westward at a rate of approximately 2 metres per day. [9]
China's population centroid has wandered within southern Henan from 1952 to 2005. Incidentally, the two end point dates are remarkably close to each other. [10] China also plots its economic centroid or center of economy/GDP, which has also wandered, and is generally located at the eastern Henan borders.
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, just 6 km southeast from the border of Tallinn. [11]
In Finland, the point of minimum aggregate travel is located in the former municipality of Hauho. [12] 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.
In Germany, the centroid of the population is located in Spangenberg, Hesse, close to Kassel. [13]
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, South Derbyshire and in 2000, it was in Appleby Parva, Leicestershire. [14] [15] Using the 2011 census the population center can be calculated at Snarestone, Swadlincote. [16]
The center of population of the entire island of Ireland is located near Kilcock, 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 and Dublin). [17] The center of population of the Republic of Ireland is located southwest of Edenderry, County Offaly. [18]
The centroid of population of Japan is in Gifu Prefecture, almost directly north of Nagoya city, and has been moving east-southeast for the past few decades. [19] Since 2010, the only large regions in Japan with significant population growth have been in Greater Tokyo and Okinawa Prefecture.
In June 2008, New Zealand's median center of population was located near Taharoa, around 100 km (65 mi) southwest of Hamilton on the North Island's west coast. [20] In 1900 it was near Nelson and has been moving steadily north (towards Auckland, the country's most populous city) ever since. [21]
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. [22]
The center of population in the Russian Federation is calculated by A. K. Gogolev to be at 56°26′N53°04′E / 56.433°N 53.067°E as of 2010, 46.5 km (28.9 mi) south-southwest of Izhevsk. [23]
The center of population of Taiwan is located in Heping District, Taichung. [24]
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, in the south-central part of the state, whereas, in 1790, it was in Kent County, Maryland, 47 miles (76 km) east-northeast of the future federal capital, Washington, D.C.
In mathematics and statistics, the arithmetic mean, arithmetic average, or just the mean or average is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a survey. The term "arithmetic mean" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic.
In statistics, a central tendency is a central or typical value for a probability distribution.
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In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any object in -dimensional Euclidean space.
The mean center of the United States population is determined by the United States Census Bureau from the results of each national census. The Bureau defines it as follows:
The concept of the center of population as used by the U.S. Census Bureau is that of a balance point. The center of population is the point at which an imaginary, weightless, rigid, and flat surface representation of the 50 states and the District of Columbia would balance if weights of identical size were placed on it so that each weight represented the location of one person. More specifically, this calculation is called the mean center of population.
There has long been debate over the exact location of the geographical centre of the United Kingdom, and its constituent countries, due to the complexity and method of the calculation, such as whether to include offshore islands, and the fact that erosion will cause the position to change over time. There are two main methods of calculating this "centre": either as the centroid of the two-dimensional shape made by the country, or as the point farthest from the boundary of the country. These two methods give quite different answers.
k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells. k-means clustering minimizes within-cluster variances, but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes squared errors, whereas only the geometric median minimizes Euclidean distances. For instance, better Euclidean solutions can be found using k-medians and k-medoids.
In geometry, the geometric median of a discrete point set in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances or absolute differences for one-dimensional data. It is also known as the spatial median, Euclidean minisum point, Torricelli point, or 1-median. It provides a measure of central tendency in higher dimensions and it is a standard problem in facility location, i.e., locating a facility to minimize the cost of transportation.
Statistical geography is the study and practice of collecting, analysing and presenting data that has a geographic or areal dimension, such as census or demographics data. It uses techniques from spatial analysis, but also encompasses geographical activities such as the defining and naming of geographical regions for statistical purposes. For example, for the purposes of statistical geography, the Australian Bureau of Statistics uses the Australian Standard Geographical Classification, a hierarchical regionalisation that divides Australia up into states and territories, then statistical divisions, statistical subdivisions, statistical local areas, and finally census collection districts.
In geography, the centroid of the two-dimensional shape of a region of the Earth's surface is known as its geographic centre or geographical centre or gravitational centre. Informally, determining the centroid is often described as finding the point upon which the shape would balance. This method is also sometimes described as the "gravitational method".
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The geographical centre of Earth is the geometric centre of all land surfaces on Earth. Geometrically defined it is the centroid of all land surfaces within the two dimensions of the Geoid surface which approximates the Earth's outer shape. The term centre of minimum distance specifies the concept more precisely as the domain is the sphere surface without boundary and not the three-dimensional body.
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