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Andorra | 600 | Foreign relations, defence and security | In the modern era, the army has consisted of a very small body of volunteers willing to undertake ceremonial duties. Uniforms and weaponry were handed down from generation to generation within families and communities. |
Andorra | 600 | Foreign relations, defence and security | The army's role in internal security was largely taken over by the formation of the Police Corps of Andorra in 1931. Brief civil disorder associated with the elections of 1933 led to assistance being sought from the French National Gendarmerie, with a detachment resident in Andorra for two months under the command of René-Jules Baulard. The Andorran Police was reformed in the following year, with eleven soldiers appointed to supervisory roles. The force consisted of six Corporals, one for each parish (although there are currently seven parishes, there were only six until 1978), plus four junior staff officers to co-ordinate action, and a commander with the rank of major. It was the responsibility of the six corporals, each in his own parish, to be able to raise a fighting force from among the able-bodied men of the parish. |
Andorra | 600 | Foreign relations, defence and security | The only permanent section of the present-day Sometent is a twelve-man ceremonial unit. However, all able-bodied men are technically available for military service, with a requirement for each family to have access to a firearm. An area weapon such as a shotgun per household is unregulated, however ranged weapons such as pistols and rifles require a license. The army has not fought for more than 700 years, and its main responsibility is to present the flag of Andorra at official ceremonial functions. According to Marc Forné Molné, Andorra's military budget is strictly from voluntary donations, and the availability of full-time volunteers. |
Andorra | 600 | Foreign relations, defence and security | In more recent times there has only been a general emergency call to the popular army of Sometent during the floods of 1982 in the Catalan Pyrenees, where 12 citizens perished in Andorra, to help the population and establish a public order along with the Local Police units. |
Andorra | 600 | Foreign relations, defence and security | Andorra maintains a small but modern and well-equipped internal police force, with around 240 police officers supported by civilian assistants. The principal services supplied by the corps are uniformed community policing, criminal detection, border control, and traffic policing. There are also small specialist units including police dogs, mountain rescue, and a bomb disposal team. |
Andorra | 600 | Foreign relations, defence and security | The Grup d'Intervenció Policia d'Andorra (GIPA) is a small special forces squad trained in counter-terrorism, and hostage recovery tasks. Although it is the closest in style to an active military force, it is part of the Police Corps, and not the army. As terrorist and hostage situations are a rare threat to the country, the GIPA is commonly assigned to prisoner escort duties, and at other times to routine policing. |
Andorra | 600 | Foreign relations, defence and security | The Andorran Fire Brigade, with headquarters at Santa Coloma, operates from four modern fire stations, and has a staff of around 120 firefighters. The service is equipped with 16 heavy appliances (fire tenders, turntable ladders, and specialist four-wheel drive vehicles), four light support vehicles (cars and vans) and four ambulances. |
Andorra | 600 | Foreign relations, defence and security | Historically, the families of the six ancient parishes of Andorra maintained local arrangements to assist each other in fighting fires. The first fire pump purchased by the government was acquired in 1943. Serious fires which lasted for two days in December 1959 led to calls for a permanent fire service, and the Andorran Fire Brigade was formed on 21 April 1961. |
Andorra | 600 | Foreign relations, defence and security | The fire service maintains full-time cover with five fire crews on duty at any time: two at the brigade's headquarters in Santa Coloma, and one crew at each of the other three fire stations. |
Andorra | 600 | Geography | Andorra consists of seven parishes: |
Andorra | 600 | Geography | Due to its location in the eastern Pyrenees mountain range, Andorra consists predominantly of rugged mountains, the highest being the Coma Pedrosa at 2,942 metres (9,652 ft), and the average elevation of Andorra is 1,996 metres (6,549 ft). These are dissected by three narrow valleys in a Y shape that combine into one as the main stream, the Gran Valira river, leaves the country for Spain (at Andorra's lowest point of 840 m or 2,756 ft). Andorra's land area is 468 km (181 sq mi). |
Andorra | 600 | Geography | Phytogeographically, Andorra belongs to the Atlantic European province of the Circumboreal Region within the Boreal Kingdom. According to the WWF, the territory of Andorra belongs to the ecoregion of Pyrenees conifer and mixed forests. Andorra had a 2018 Forest Landscape Integrity Index mean score of 4.45/10, ranking it 127th globally out of 172 countries. |
Andorra | 600 | Geography | The whole country has been recognised as a single Important Bird Area (IBA) by BirdLife International, because it is important for forest and mountain birds and supports populations of red-billed choughs, citril finches and rock buntings. |
Andorra | 600 | Geography | Andorra has alpine, continental and oceanic climates, depending on altitude. Its higher elevation means there is, on average, more snow in winter and it is slightly cooler in summer. The diversity of landmarks, the different orientation of the valleys and the irregularity relief typical of the Mediterranean climates make the country have a great diversity of microclimates that hinder the general dominance of the high mountain climate. The great differences of altitude in the minimum and maximum points, together with the influence of a Mediterranean climate, develop the climate of the Andorran Pyrenees. |
Andorra | 600 | Geography | When in precipitation, a global model characterized by convective and abundant rains can be defined during spring and summer, which can last until autumn (May, June and August are usually the rainiest months). In winter, however, it is less rainy, except in the highlands, subject to the influence of fronts from the Atlantic, which explains the great amount of snowfall in the Andorran mountains. The temperature regime is characterized, broadly, by a temperate summer and a long and cold winter, in accordance with the mountainous condition of the Principality. |
Andorra | 600 | Economy | Tourism, the mainstay of Andorra's economy, accounts for roughly 80% of GDP. An estimated 10.2 million tourists visit annually, attracted by Andorra's duty-free status and by its summer and winter resorts. |
Andorra | 600 | Economy | One of the main sources of income in Andorra is tourism from ski resorts which total over 175 km (109 mi) of ski ground. The sport brings in over 7 million visitors annually and an estimated 340 million euros per year, sustaining 2,000 direct and 10,000 indirect jobs at present since 2007. |
Andorra | 600 | Economy | The banking sector, with its tax haven status, also contributes substantially to the economy with revenues raised exclusively through import tariffs (the financial and insurance sector accounts for approximately 19% of GDP). However, during the European sovereign-debt crisis of the 21st century, the tourist industry suffered a decline, partly caused by a drop in the prices of goods in Spain, undercutting duty-free shopping and increasing unemployment. On 1 January 2012, a business tax of 10% was introduced, followed by a sales tax of 2% a year later, which raised just over 14 million euros in its first quarter. |
Andorra | 600 | Economy | Agricultural production is limited; only 1.7% of the land is arable, and most food has to be imported. Some tobacco is grown locally. The principal livestock activity is domestic sheep raising. Manufacturing output consists mainly of cigarettes, cigars, and furniture. Andorra's natural resources include hydroelectric power, mineral water, timber, iron ore, and lead. |
Andorra | 600 | Economy | Andorra is not a member of the European Union, but enjoys a special relationship with it, such as being treated as an EU member for trade in manufactured goods (no tariffs) and as a non-EU member for agricultural products. Andorra lacked a currency of its own and used both the French franc and the Spanish peseta in banking transactions until 31 December 1999, when both currencies were replaced by the EU's single currency, the euro. Coins and notes of both the franc and the peseta remained legal tender in Andorra until 31 December 2002. Andorra negotiated to issue its own euro coins, beginning in 2014. |
Andorra | 600 | Economy | Andorra has historically had one of the world's lowest unemployment rates. In 2019 it stood at 2%. |
Andorra | 600 | Economy | On 31 May 2013, it was announced that Andorra intended to legislate for the introduction of an income tax by the end of June, against a background of increasing dissatisfaction with the existence of tax havens among EU members. The announcement was made following a meeting in Paris between the Prime Minister Antoni Martí and the French President and Prince of Andorra François Hollande. Hollande welcomed the move as part of a process of Andorra "bringing its taxation in line with international standards". |
Andorra | 600 | Economy | By the mid-2010s, the financial system comprised five banking groups, one specialised credit entity, eight investment undertaking management entities, three asset management companies, and 29 insurance companies, 14 of which are branches of foreign insurance companies authorised to operate in the principality. The last mergers between banks took place in 2022, bringing the Andorran financial sector to currently have 3 active banking groups. |
Andorra | 600 | Demographics | The population of Andorra is estimated at 79,034 (2021). The Andorrans are a Romance ethnic group of originally Catalan descent. The population has grown from 5,000 in 1900. |
Andorra | 600 | Demographics | Two-thirds of residents lack Andorran nationality and do not have the right to vote in communal elections. Moreover, they are not allowed to be elected as prime minister or to own more than 33% of the capital stock of a privately held company. |
Andorra | 600 | Demographics | According to mother tongue percentage statistics by the Andorran Government released in 2018: |
Andorra | 600 | Demographics | Mother tongue Source: Coneixements i Usos Lingüístics de la Població d'Andorra (1995–2022) |
Andorra | 600 | Demographics | The historic and official language is Catalan, a Romance language. The Andorran government encourages the use of Catalan. It funds a Commission for Catalan Toponymy in Andorra (Catalan: Comissió de Toponímia d'Andorra), and provides free Catalan classes to assist immigrants. Andorran television and radio stations use Catalan. |
Andorra | 600 | Demographics | Because of immigration, historical links, and close geographic proximity, Spanish, Portuguese and French are commonly spoken. Most Andorran residents can speak one or more of these, in addition to Catalan. English is less commonly spoken among the general population, though it is understood to varying degrees in the major tourist resorts. Andorra is one of only four European countries (together with France, Monaco, and Turkey) that have never signed the Council of Europe Framework Convention on National Minorities. |
Andorra | 600 | Demographics | Religion of Andorra |
Andorra | 600 | Demographics | Few official statistics are available on religion; estimates of the Catholic population in 2020 range from 89.5% and 99.21%. The patron saint is Our Lady of Meritxell. There are also members of various Protestant denominations and small numbers of Hindus, and Bahá'ís, In 2022 there were approximately 2000 Muslims and roughly 100 Jews. |
Andorra | 600 | Education | Children between the ages of 6 and 16 are required by law to have full-time education. Education up to secondary level is provided free of charge by the government. |
Andorra | 600 | Education | There are three systems of school, Andorran, French and Spanish, which use Catalan, French and Spanish languages respectively, as the main language of instruction. Parents may choose which system their children attend. All schools are built and maintained by Andorran authorities, but teachers in the French and Spanish schools are paid for the most part by France and Spain. 39% of Andorran children attend Andorran schools, 33% attend French schools, and 28% Spanish schools. |
Andorra | 600 | Education | The Universitat d'Andorra (UdA) is the state public university and is the only university in Andorra. It was established in 1997. The university provides first-level degrees in nursing, computer science, business administration, and educational sciences, in addition to higher professional education courses. The only two graduate schools in Andorra are the Nursing School and the School of Computer Science, the latter having a PhD programme. |
Andorra | 600 | Education | The geographical complexity of the country as well as the small number of students prevents the University of Andorra from developing a full academic programme, and it serves principally as a centre for virtual studies, connected to Spanish and French universities. The Virtual Studies Centre (Centre d'Estudis Virtuals) at the university runs approximately 20 different academic degrees at both undergraduate and postgraduate levels in fields including tourism, law, Catalan philology, humanities, psychology, political sciences, audiovisual communication, telecommunications engineering, and East Asia studies. The centre also runs various postgraduate programmes and continuing-education courses for professionals. |
Andorra | 600 | Transport | Until the 20th century, Andorra had very limited transport links to the outside world, and development of the country was affected by its physical isolation. Even now, the nearest major airports at Toulouse and Barcelona are both three hours' drive from Andorra. |
Andorra | 600 | Transport | Andorra has a road network of 279 km (173 mi), of which 76 km (47 mi) is unpaved. The two main roads out of Andorra la Vella are the CG-1 to the Spanish border near Sant Julià de Lòria, and the CG-2 to the French border via the Envalira Tunnel near El Pas de la Casa. Bus services cover all metropolitan areas and many rural communities, with services on most major routes running half-hourly or more frequently during peak travel times. There are frequent long-distance bus services from Andorra to Barcelona and Toulouse, plus a daily tour from the former city. Bus services mostly are run by private companies, but some local ones are operated by the government. |
Andorra | 600 | Transport | There are no airports for fixed-wing aircraft within Andorra's borders but there are, however, heliports in La Massana (Camí Heliport), Arinsal and Escaldes-Engordany with commercial helicopter services and an airport located in the neighbouring Spanish comarca of Alt Urgell, 12 kilometres (7.5 miles) south of the Andorran-Spanish border. Since July 2015, Andorra–La Seu d'Urgell Airport has operated commercial flights to Madrid and Palma de Mallorca, and is the main hub for Andorra Airlines. |
Andorra | 600 | Transport | Nearby airports located in Spain and France provide access to international flights for the principality. The nearest airports are at Perpignan, France (156 kilometres or 97 miles from Andorra) and Lleida, Spain (160 kilometres or 99 miles from Andorra). The largest nearby airports are at Toulouse, France (165 kilometres or 103 miles from Andorra) and Barcelona, Spain (215 kilometres or 134 miles from Andorra). There are hourly bus services from both Barcelona and Toulouse airports to Andorra. |
Andorra | 600 | Transport | The nearest railway station is Andorre-L'Hospitalet station 10 km (6 mi) east of Andorra which is on the 1,435 mm (4 ft 8+1⁄2 in)-gauge line from Latour-de-Carol (25 km or 16 mi) southeast of Andorra, to Toulouse and on to Paris by the French high-speed trains. This line is operated by the SNCF. Latour-de-Carol has a scenic 1,000 mm (3 ft 3+3⁄8 in) metre gauge trainline to Villefranche-de-Conflent, as well as the SNCF's 1,435 mm gauge line connecting to Perpignan, and the Renfe's 1,668 mm (5 ft 5+21⁄32 in) -gauge line to Barcelona. There are also direct Intercités de Nuit trains between L'Hospitalet-près-l'Andorre and Paris on certain dates. |
Andorra | 600 | Media and telecommunications | In Andorra, mobile and fixed telephone and internet services are operated exclusively by the Andorran national telecommunications company, SOM, also known as Andorra Telecom (STA). The same company also manages the technical infrastructure for national broadcasting of digital television and radio. In 2010 Andorra became the first country to provide a direct optical fiber link to all homes (FTTH) and businesses. |
Andorra | 600 | Media and telecommunications | The first commercial radio station to broadcast was Radio Andorra, which was active from 1939 to 1981. On 12 October 1989, the General Council established radio and television as essential public services creating and managing the entity ORTA, becoming on 13 April 2000, in the public company Ràdio i Televisió d'Andorra (RTVA). In 1990, the public radio was founded on the Radio Nacional d'Andorra. As an autochthonous television channel, there is only the national public television network Andorra Televisió, created in 1995. Additional TV and radio stations from Spain and France are available via digital terrestrial television and IPTV. |
Andorra | 600 | Media and telecommunications | There are three national newspapers, Diari d'Andorra, El Periòdic d'Andorra, and Bondia as well as several local newspapers. The history of the Andorran press begins in the period between 1917 and 1937 with the appearance of several periodicals papers such as Les Valls d'Andorra (1917), Nova Andorra (1932) and Andorra Agrícola (1933). In 1974, the Poble Andorrà became the first regular newspaper in Andorra. There is also an amateur radio society and news agency ANA with independent management. |
Andorra | 600 | Culture | Andorra is home to folk dances like the contrapàs and marratxa, which survive in Sant Julià de Lòria especially. Andorran folk music has similarities to the music of its neighbours, but is especially Catalan in character, especially in the presence of dances such as the sardana. Other Andorran folk dances include contrapàs in Andorra la Vella and Saint Anne's dance in Escaldes-Engordany. Andorra's national holiday is Our Lady of Meritxell Day, 8 September. |
Andorra | 600 | Culture | Among the more important festivals and traditions are the Canólich Gathering in May, the Roser d'Ordino in July, the Meritxell Day (National Day of Andorra), the Andorra la Vella Fair, the Sant Jordi Day, the Santa Llúcia Fair, the Festivity from La Candelera to Canillo, the Carnival of Encamp, the sung of caramelles, the Festivity of Sant Esteve and the Festa del Poble. |
Andorra | 600 | Culture | Andorra participated regularly in the Eurovision Song Contest between 2004 and 2009, being the only participating country presenting songs in Catalan. |
Andorra | 600 | Culture | In popular folklore, the best-known Andorran legends are the legend of Charlemagne, according to which this Frankish King would have founded the country, the White Lady of Auvinyà, the Buner d'Ordino, the legend of Engolasters Lake and the legend of Our Lady of Meritxell. |
Andorra | 600 | Culture | Andorran gastronomy is mainly Catalan, although it has also adopted other elements of French and Italian cuisines. The cuisine of the country has similar characteristics with the neighbours of Cerdanya and Alt Urgell, with whom it has strong cultural ties. Andorra's cuisine is marked by its nature as mountain valleys. Typical dishes of the country are quince all-i-oli, duck with winter pear, roast lamb with nuts, pork civet, massegada cake, escarole with pears, duck confit and mushrooms, escudella, spinach with raisins and pine nuts, jelly marmalade, stuffed murgues (mushrooms) with pork, dandelion salad, and Andorran river trout. To drink, mulled wine and beer are also popular. Some of the dishes are very common in the mountainous regions of Catalonia, such as trinxat, embotits, cooked snails, rice with mushrooms, mountain rice and mató. |
Andorra | 600 | Culture | Pre-Romanesque and Romanesque art are one of the most important artistic manifestations and characteristics of the Principality. The Romanesque one allows to know the formation of the parochial communities, the relations of (social and political) power and the national culture. There are a total of forty Romanesque churches that stand out as being small austere ornamentation constructions, as well as bridges, fortresses and manor houses of the same period. |
Andorra | 600 | Culture | Summer solstice fire festivals in the Pyrenees was included as UNESCO Intangible cultural heritage in 2015. Also the Madriu-Perafita-Claror Valley became Andorra's first, and to date its only, UNESCO World Heritage Site in 2004, with a small extension in 2006. |
Andorra | 600 | Culture | Andorra is famous for the practice of winter sports. Andorra has the largest territory of ski slopes in the Pyrenees (3100 hectares and about 350 km of slopes) and two ski resorts. Grandvalira is the largest and most popular resort. Other popular sports played in Andorra include football, rugby union, basketball, and roller hockey. |
Andorra | 600 | Culture | For roller hockey, Andorra usually plays in CERH Euro Cup and in FIRS Roller Hockey World Cup. In 2011, Andorra was the host country to the 2011 European League Final Eight. |
Andorra | 600 | Culture | The country is represented in association football by the Andorra national football team. The team gained its first competitive win in a European Championship qualifier on 11 October 2019, against Moldova. Football is governed in Andorra by the Andorran Football Federation – founded in 1994, it organizes the national competitions of association football (Primera Divisió, Copa Constitució and Supercopa) and futsal. Andorra was admitted to UEFA and FIFA in the same year, 1996. FC Andorra, a club based in Andorra la Vella founded in 1942, compete in the Spanish football league system. |
Andorra | 600 | Culture | Rugby is a traditional sport in Andorra, mainly influenced by the popularity in southern France. The Andorra national rugby union team, nicknamed Els Isards, plays on the international stage in rugby union and rugby sevens. VPC Andorra XV is a rugby team based in Andorra la Vella, which actually plays in the French championship. |
Andorra | 600 | Culture | Basketball popularity has increased in the country since the 1990s, when the Andorran team BC Andorra played in the top league of Spain (Liga ACB). After 18 years the club returned to the top league in 2014. |
Andorra | 600 | Culture | Other sports practised in Andorra include cycling, volleyball, judo, Australian Rules football, handball, swimming, gymnastics, tennis, and motorsports. In 2012, Andorra raised its first national cricket team and played a home match against the Dutch Fellowship of Fairly Odd Places Cricket Club, the first match played in the history of Andorra at an altitude of 1,300 metres (4,300 ft). |
Andorra | 600 | Culture | Andorra first participated at the Olympic Games in 1976. The country has appeared in every Winter Olympic Games since 1976. Andorra competes in the Games of the Small States of Europe, being twice the host country, in 1991 and 2005. |
Andorra | 600 | Culture | As one of the Catalan Countries, Andorra is home to a team of castellers, or Catalan human tower builders. The Castellers d'Andorra [ca], based in the town of Santa Coloma d'Andorra, are recognized by the Coordinadora de Colles Castelleres de Catalunya [ca], the governing body of castells. |
Andorra | 600 | External links | 42°33′N 1°35′E / 42.550°N 1.583°E / 42.550; 1.583 |
Arithmetic mean | 612 | In mathematics and statistics, the arithmetic mean ( /ˌærɪθˈmɛtɪk ˈmiːn/ arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context is clear) 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. |
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Arithmetic mean | 612 | In addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology, history, and almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population. |
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Arithmetic mean | 612 | While the arithmetic mean is often used to report central tendencies, it is not a robust statistic: it is greatly influenced by outliers (values much larger or smaller than most others). For skewed distributions, such as the distribution of income for which a few people's incomes are substantially higher than most people's, the arithmetic mean may not coincide with one's notion of "middle". In that case, robust statistics, such as the median, may provide a better description of central tendency. |
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Arithmetic mean | 612 | Definition | Given a data set X = { x 1 , … , x n } {\displaystyle X=\{x_{1},\ldots ,x_{n}\}} , the arithmetic mean (also mean or average), denoted x ¯ {\displaystyle {\bar {x}}} (read x {\displaystyle x} bar), is the mean of the n {\displaystyle n} values x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} . |
Arithmetic mean | 612 | Definition | The arithmetic mean is a data set's most commonly used and readily understood measure of central tendency. In statistics, the term average refers to any measurement of central tendency. The arithmetic mean of a set of observed data is equal to the sum of the numerical values of each observation, divided by the total number of observations. Symbolically, for a data set consisting of the values x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} , the arithmetic mean is defined by the formula: |
Arithmetic mean | 612 | Definition | (For an explanation of the summation operator, see summation.) |
Arithmetic mean | 612 | Definition | For example, if the monthly salaries of 10 {\displaystyle 10} employees are { 2500 , 2700 , 2400 , 2300 , 2550 , 2650 , 2750 , 2450 , 2600 , 2400 } {\displaystyle \{2500,2700,2400,2300,2550,2650,2750,2450,2600,2400\}} , then the arithmetic mean is: |
Arithmetic mean | 612 | Definition | If the data set is a statistical population (i.e., consists of every possible observation and not just a subset of them), then the mean of that population is called the population mean and denoted by the Greek letter μ {\displaystyle \mu } . If the data set is a statistical sample (a subset of the population), it is called the sample mean (which for a data set X {\displaystyle X} is denoted as X ¯ {\displaystyle {\overline {X}}} ). |
Arithmetic mean | 612 | Definition | The arithmetic mean can be similarly defined for vectors in multiple dimensions, not only scalar values; this is often referred to as a centroid. More generally, because the arithmetic mean is a convex combination (meaning its coefficients sum to 1 {\displaystyle 1} ), it can be defined on a convex space, not only a vector space. |
Arithmetic mean | 612 | Motivating properties | The arithmetic mean has several properties that make it interesting, especially as a measure of central tendency. These include: |
Arithmetic mean | 612 | Contrast with median | The arithmetic mean may be contrasted with the median. The median is defined such that no more than half the values are larger, and no more than half are smaller than it. If elements in the data increase arithmetically when placed in some order, then the median and arithmetic average are equal. For example, consider the data sample { 1 , 2 , 3 , 4 } {\displaystyle \{1,2,3,4\}} . The mean is 2.5 {\displaystyle 2.5} , as is the median. However, when we consider a sample that cannot be arranged to increase arithmetically, such as { 1 , 2 , 4 , 8 , 16 } {\displaystyle \{1,2,4,8,16\}} , the median and arithmetic average can differ significantly. In this case, the arithmetic average is 6.2 {\displaystyle 6.2} , while the median is 4 {\displaystyle 4} . The average value can vary considerably from most values in the sample and can be larger or smaller than most. |
Arithmetic mean | 612 | Contrast with median | There are applications of this phenomenon in many fields. For example, since the 1980s, the median income in the United States has increased more slowly than the arithmetic average of income. |
Arithmetic mean | 612 | Generalizations | A weighted average, or weighted mean, is an average in which some data points count more heavily than others in that they are given more weight in the calculation. For example, the arithmetic mean of 3 {\displaystyle 3} and 5 {\displaystyle 5} is 3 + 5 2 = 4 {\displaystyle {\frac {3+5}{2}}=4} , or equivalently 3 1 2 + 5 1 2 = 4 {\displaystyle 3{\frac {1}{2}}+5{\frac {1}{2}}=4} . In contrast, a weighted mean in which the first number receives, for example, twice as much weight as the second (perhaps because it is assumed to appear twice as often in the general population from which these numbers were sampled) would be calculated as 3 2 3 + 5 1 3 = 11 3 {\displaystyle 3{\frac {2}{3}}+5{\frac {1}{3}}={\frac {11}{3}}} . Here the weights, which necessarily sum to one, are 2 3 {\displaystyle {\frac {2}{3}}} and 1 3 {\displaystyle {\frac {1}{3}}} , the former being twice the latter. The arithmetic mean (sometimes called the "unweighted average" or "equally weighted average") can be interpreted as a special case of a weighted average in which all weights are equal to the same number ( 1 2 {\displaystyle {\frac {1}{2}}} in the above example and 1 n {\displaystyle {\frac {1}{n}}} in a situation with n {\displaystyle n} numbers being averaged). |
Arithmetic mean | 612 | Generalizations | If a numerical property, and any sample of data from it, can take on any value from a continuous range instead of, for example, just integers, then the probability of a number falling into some range of possible values can be described by integrating a continuous probability distribution across this range, even when the naive probability for a sample number taking one certain value from infinitely many is zero. In this context, the analog of a weighted average, in which there are infinitely many possibilities for the precise value of the variable in each range, is called the mean of the probability distribution. The most widely encountered probability distribution is called the normal distribution; it has the property that all measures of its central tendency, including not just the mean but also the median mentioned above and the mode (the three Ms), are equal. This equality does not hold for other probability distributions, as illustrated for the log-normal distribution here. |
Arithmetic mean | 612 | Generalizations | Particular care is needed when using cyclic data, such as phases or angles. Taking the arithmetic mean of 1° and 359° yields a result of 180°. This is incorrect for two reasons: |
Arithmetic mean | 612 | Generalizations | In general application, such an oversight will lead to the average value artificially moving towards the middle of the numerical range. A solution to this problem is to use the optimization formulation (that is, define the mean as the central point: the point about which one has the lowest dispersion) and redefine the difference as a modular distance (i.e., the distance on the circle: so the modular distance between 1° and 359° is 2°, not 358°). |
Arithmetic mean | 612 | Symbols and encoding | The arithmetic mean is often denoted by a bar (vinculum or macron), as in x ¯ {\displaystyle {\bar {x}}} . |
Arithmetic mean | 612 | Symbols and encoding | Some software (text processors, web browsers) may not display the "x̄" symbol correctly. For example, the HTML symbol "x̄" combines two codes — the base letter "x" plus a code for the line above (̄ or ¯). |
Arithmetic mean | 612 | Symbols and encoding | In some document formats (such as PDF), the symbol may be replaced by a "¢" (cent) symbol when copied to a text processor such as Microsoft Word. |
American Football Conference | 615 | The American Football Conference (AFC) is one of the two conferences of the National Football League (NFL), the highest professional level of American football in the United States. The AFC and its counterpart, the National Football Conference (NFC), each contain 16 teams with 4 divisions. Both conferences were created as part of the 1970 merger between the National Football League, and the American Football League (AFL). All ten of the AFL teams, and three NFL teams, became members of the new AFC, with the remaining thirteen NFL teams forming the NFC. A series of league expansions and division realignments have occurred since the merger, thus making the current total of 16 teams in each conference. The current AFC champions are the Kansas City Chiefs, who defeated the Cincinnati Bengals in the 2022 season's AFC Championship Game for their third conference championship. |
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American Football Conference | 615 | Teams | Like the NFC, the conference has 16 teams organized into four divisions each with four teams: East, North, South and West. |
American Football Conference | 615 | Season structure | Currently, the fourteen opponents each team faces over the 17-game regular season schedule are set using a pre-determined formula: |
American Football Conference | 615 | Season structure | Each AFC team plays the other teams in their respective division twice (home and away) during the regular season, in addition to eleven other games assigned to their schedule by the NFL: three games are assigned on the basis of a particular team's final divisional standing from the previous season, and the remaining eight games are split between the roster of two other NFL divisions. This assignment shifts each year and will follow a standard cycle. Using the 2023 regular season schedule as an example, each team in the AFC West plays against every team in the AFC East and NFC North. In this way, non-divisional competition will be mostly among common opponents – the exception being the three games assigned based on the team's prior-season divisional standing. |
American Football Conference | 615 | Season structure | At the end of each season, the four division winners and three wild cards (non-division winners with best regular season record) in the AFC qualify for the playoffs. The AFC playoffs culminate in the AFC Championship Game, with the winner receiving the Lamar Hunt Trophy. The AFC champion then plays the NFC champion in the Super Bowl. |
American Football Conference | 615 | History | Both the AFC and the NFC were created after the NFL merged with the American Football League (AFL) in 1970. The AFL began play in 1960 with eight teams, and added two more expansion clubs (the Miami Dolphins in 1966 and the Cincinnati Bengals in 1968) before the merger. In order to equalize the number of teams in each conference, three NFL teams that predated the AFL's launch (the Cleveland Browns, Pittsburgh Steelers, and the then-Baltimore Colts) joined the ten former AFL teams to form the AFC. The two AFL divisions AFL East and AFL West were more or less intact, while the NFL's Century Division, in which the Browns and the Steelers had played since 1967, was moved from the NFL to become the new AFC Central. Upon the completion of the merger of the AFL and NFL in 1970, the newly minted American Football Conference had already agreed upon their divisional setup along mostly geographical lines for the 1970 season; the National Football Conference, however, could not agree upon their setup, and one was chosen from a fishbowl on January 16, 1970. |
American Football Conference | 615 | History | Since the merger, five expansion teams have joined the AFC and two have left, thus making the current total 16. When the Seattle Seahawks and the Tampa Bay Buccaneers joined the league in 1976, they were temporarily placed in the NFC and AFC respectively. This arrangement lasted for one season only before the two teams switched conferences. The Seahawks eventually returned to the NFC as a result of the 2002 realignment. The expansion Jacksonville Jaguars joined the AFC in 1995. There have been five teams that have relocated at least once. In 1984, the Baltimore Colts relocated to Indianapolis. In 1995, the Cleveland Browns had attempted to move to Baltimore; the resulting dispute between Cleveland and the team led to Modell establishing the Baltimore Ravens with the players and personnel from the Browns, while the Browns were placed in suspended operations before they were reinstated by the NFL. The Ravens were treated as an expansion team. |
American Football Conference | 615 | History | In California, the Oakland Raiders relocated to Los Angeles in 1982, back to Oakland in 1995, and then to Las Vegas in 2020, while the San Diego Chargers returned to Los Angeles in 2017 after 56 years in San Diego. |
American Football Conference | 615 | History | The Houston Oilers moved to Tennessee in 1997, where they were renamed the Tennessee Oilers. The team would change its name again, two years later, to the Tennessee Titans. |
American Football Conference | 615 | History | The NFL would again expand in 2002, adding the Houston Texans to the AFC. With the exception of the aforementioned relocations since that time, the divisional setup has remained static ever since. |
American Football Conference | 615 | History | Between 1995 and 2022, the AFC has sent only 9 of its 16 teams to the Super Bowl: New England Patriots (10 times), Pittsburgh Steelers (4 times), Denver Broncos (4 times), Baltimore Ravens (2 times), Indianapolis Colts (2 times), Kansas City Chiefs (3 times), Cincinnati Bengals (1 time), Las Vegas Raiders (1 time), Tennessee Titans (1 time). By contrast, the NFC has sent 13 of the 16 NFC teams during that same time frame with only the Detroit Lions, Minnesota Vikings, and Washington Commanders missing out on an appearance in the Super Bowl. 17 of the 19 AFC champions from 2001 to 2019 have started one of just three quarterbacks - Tom Brady, Peyton Manning and Ben Roethlisberger - in the Super Bowl. The AFC has started 7 quarterbacks in the last 20 Super Bowls, while the NFC has started 16. |
American Football Conference | 615 | Logo | The merged league created a new logo for the AFC that took elements of the old AFL logo, specifically the "A" and the six stars surrounding it. The NFC also adopted a logo in 1970 which like the AFL and AFC logos also contained only the first letter as opposed to a full abbreviation, but with only three stars (to represent the then-three divisions of the Conference). The AFC logo basically remained unchanged from 1970 to 2009. The 2010 NFL season introduced an updated AFC logo, with the most notable revision being the removal of two stars (leaving four representing the four divisions of the AFC), and moving the stars inside the letter, similar to the NFC logo, which itself was updated at the same time to add a fourth star. |
American Football Conference | 615 | Television | NBC aired the AFC's Sunday afternoon and playoff games from 1970 through the 1997 season. From 1998 to 2013, CBS was the primary broadcast rightsholder to the AFC; in those years, all interconference games in which the AFC team was the visiting team were broadcast on either NBC or CBS. Since 2014, the cross-flex policy allows select AFC games (that involve them playing an NFC team at home or intraconference games) to be moved from CBS to Fox. Since 1990, select AFC playoff games have been seen on ABC or ESPN. |
American Football Conference | 615 | See also | AFC Divisions |
American Football Conference | 615 | See also | AFC Division Rivals |
American Football Conference | 615 | See also | AFC East |
American Football Conference | 615 | See also | AFC North |
American Football Conference | 615 | See also | AFC South Rivals |
American Football Conference | 615 | See also | AFC West Rivals |
American Football Conference | 615 | See also | AFC Interdivisional Rivals |
American Football Conference | 615 | See also | AFC Television Network |
Animal Farm | 620 | Animal Farm is a beast fable, in the form of a satirical allegorical novella, by George Orwell, first published in England on 17 August 1945. It tells the story of a group of anthropomorphic farm animals who rebel against their human farmer, hoping to create a society where the animals can be equal, free, and happy. Ultimately, the rebellion is betrayed and, under the dictatorship of a pig named Napoleon, the farm ends up in a state as bad as it was before. |
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