1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. It is also the first of the infinite sequence of natural numbers, followed by 2.
| ||||
---|---|---|---|---|
Cardinal | one | |||
Ordinal | 1st (first) | |||
Numeral system | unary | |||
Factorization | ∅ | |||
Divisors | 1 | |||
Greek numeral | Α´ | |||
Roman numeral | I | |||
Roman numeral (unicode) | Ⅰ, ⅰ | |||
Binary | 1_{2} | |||
Ternary | 1_{3} | |||
Quaternary | 1_{4} | |||
Quinary | 1_{5} | |||
Senary | 1_{6} | |||
Octal | 1_{8} | |||
Duodecimal | 1_{12} | |||
Hexadecimal | 1_{16} | |||
Vigesimal | 1_{20} | |||
Base 36 | 1_{36} | |||
Greek numeral | α' | |||
Persian | ١ | |||
Arabic & Kurdish | ١ | |||
Urdu | ||||
Sindhi | ١ | |||
Assamese & Bengali | ১ | |||
Chinese numeral | 一/弌/壹 | |||
Devanāgarī | १ | |||
Ge'ez | ፩ | |||
Georgian | Ⴁ/ⴁ/ბ(Bani) | |||
Hebrew | א | |||
Japanese numeral | 一/壱 | |||
Kannada | ೧ | |||
Khmer | ១ | |||
Korean | 일/하나 | |||
Malayalam | ൧ | |||
Thai | ๑ | |||
Tamil | ௧ |
The word one can be used as a noun, an adjective and a pronoun.^{[1]}
It comes from the English word an,^{[1]} which comes from the Proto-Germanic root *ainaz.^{[1]} The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-.^{[1]}
Compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish en, Dutch een, German eins and Old Norse einn.
Compare the Proto-Indo-European root *oi-no- (which means "one, single"^{[1]}) to Greek oinos (which means "ace" on dice^{[1]}), Latin unus (one^{[1]}), Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin and Breton un (one^{[1]}).
One, sometimes referred to as unity,^{[2]} is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number.
Any number multiplied by one remains that number, as one is the identity for multiplication. As a result, 1 is its own factorial, its own square and square root, its own cube and cube root, and so on. One is also the result of the empty product, as any number multiplied by one is itself. It is also the only natural number that is neither composite nor prime with respect to division, but instead considered a unit (meaning of ring theory).
The glyph used today in the Western world to represent the number 1, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom, traces its roots back to the Indians, who wrote 1 as a horizontal line, much like the Chinese character 一. The Gupta wrote it as a curved line, and the Nagari sometimes added a small circle on the left (rotated a quarter turn to the right, this 9-look-alike became the present day numeral 1 in the Gujarati and Punjabi scripts). The Nepali also rotated it to the right but kept the circle small.^{[3]} This eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. In some countries, the serif at the top is sometimes extended into a long upstroke, sometimes as long as the vertical line, which can lead to confusion with the glyph for seven in other countries. Where the 1 is written with a long upstroke, the number 7 has a horizontal stroke through the vertical line.
While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, the character usually is of x-height, as, for example, in
Many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used, while it may be for decorative purposes.
Mathematically, 1 is:
Tallying is often referred to as "base 1", since only one mark – the tally itself – is needed. This is more formally referred to as a unary numeral system. Unlike base 2 or base 10, this is not a positional notation.
Since the base 1 exponential function (1^{x}) always equals 1, its inverse does not exist (which would be called the logarithm base 1 if it did exist).
There are two ways to write the real number 1 as a recurring decimal: as 1.000..., and as 0.999....
Formalizations of the natural numbers have their own representations of 1:
In a multiplicative group or monoid, the identity element is sometimes denoted 1, but e (from the German Einheit, "unity") is also traditional. However, 1 is especially common for the multiplicative identity of a ring, i.e., when an addition and 0 are also present. When such a ring has characteristic n not equal to 0, the element called 1 has the property that n1 = 1n = 0 (where this 0 is the additive identity of the ring). Important examples are finite fields.
1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few.
In many mathematical and engineering problems, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. Likewise, vectors are often normalized to give unit vectors, that is vectors of magnitude one, because these often have more desirable properties. Functions, too, are often normalized by the condition that they have integral one, maximum value one, or square integral one, depending on the application.
Because of the multiplicative identity, if f(x) is a multiplicative function, then f(1) must equal 1.
It is also the first and second number in the Fibonacci sequence (0 is the zeroth) and is the first number in many other mathematical sequences.
1 is neither a prime number nor a composite number, but a unit (meaning of ring theory), like −1 and, in the Gaussian integers, i and −i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units. (For example, 4 = 2^{2}, but if units are included, is also equal to, say, (−1)^{6} × 1^{23} × 2^{2}, among infinitely many similar "factorizations".)
The definition of a field requires that 1 must not be equal to 0. Thus, there are no fields of characteristic 1. Nevertheless, abstract algebra can consider the field with one element, which is not a singleton and is not a set at all.
1 is the only positive integer divisible by exactly one positive integer (whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers). 1 was formerly considered prime by some mathematicians, using the definition that a prime is divisible only by 1 and itself. However, this complicates the fundamental theorem of arithmetic, so modern definitions exclude units.
By definition, 1 is the magnitude, absolute value, or norm of a unit complex number, unit vector, and a unit matrix (more usually called an identity matrix). Note that the term unit matrix is sometimes used to mean something quite different.
By definition, 1 is the probability of an event that is almost certain to occur.
1 is the most common leading digit in many sets of data, a consequence of Benford's law.
1 is the only known Tamagawa number for a simply connected algebraic group over a number field.
The generating function that has all coefficients 1 is given by
This power series converges and has finite value if and only if, .
In category theory, 1 is sometimes used to denote the terminal object of a category.
In number theory, 1 is the value of Legendre's constant, which was introduced in 1808 by Adrien-Marie Legendre in expressing the asymptotic behavior of the prime-counting function. Legendre's constant was originally conjectured to be approximately 1.08366, but was proven to equal exactly 1 in 1899.
Multiplication | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 50 | 100 | 1000 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 × x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 50 | 100 | 1000 |
Division | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 ÷ x | 1 | 0.5 | 0.3 | 0.25 | 0.2 | 0.16 | 0.142857 | 0.125 | 0.1 | 0.1 | 0.09 | 0.083 | 0.076923 | 0.0714285 | 0.06 | |
x ÷ 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Exponentiation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1^{x} | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
x^{1} | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
In the philosophy of Plotinus and a number of other neoplatonists, The One is the ultimate reality and source of all existence. Philo of Alexandria (20 BC – AD 50) regarded the number one as God's number, and the basis for all numbers ("De Allegoriis Legum," ii.12 [i.66]).
The 2015–16 UEFA Champions League was the 61st season of Europe's premier club football tournament organised by UEFA, and the 24th season since it was renamed from the European Champion Clubs' Cup to the UEFA Champions League. Barcelona were the title holders, but were eliminated by Atlético Madrid in the quarter-finals.
The 2016 UEFA Champions League Final was played between Real Madrid and Atlético Madrid at the San Siro in Milan, Italy. It was the second time in the tournament's history that both finalists were from the same city, after the same clubs faced each other in the 2014 final. Real Madrid defeated Atlético Madrid 5–3 on penalties (1–1 after extra time) in the final to win a record-extending eleventh European Cup/Champions League title.
As the winners of the 2015–16 UEFA Champions League, Real Madrid qualified as the UEFA representative at the 2016 FIFA Club World Cup in Japan (their third Club World Cup appearance), and also earned the right to play against the winners of the 2015–16 UEFA Europa League, Sevilla, in the 2016 UEFA Super Cup.
2016–17 UEFA Champions LeagueThe 2016–17 UEFA Champions League was the 62nd season of Europe's premier club football tournament organised by UEFA, and the 25th season since it was renamed from the European Champion Clubs' Cup to the UEFA Champions League.
The final was played between Juventus and Real Madrid at the Millennium Stadium in Cardiff, Wales. It was the second time that the two teams faced each other in the competition's decisive match, having previously met in the 1998 final. Real Madrid, the defending champions, beat Juventus 4–1 to win a record-extending 12th title. With this victory, Real Madrid became the first team to successfully defend their title in the Champions League era, and the first to do so since Milan in 1990.
As winners, Real Madrid qualified as the UEFA representative for the 2017 FIFA Club World Cup in the United Arab Emirates, and also earned the right to play against the winners of the 2016–17 UEFA Europa League, Manchester United, in the 2017 UEFA Super Cup.
2017–18 UEFA Champions LeagueThe 2017–18 UEFA Champions League was the 63rd season of Europe's premier club football tournament organised by UEFA, the 26th season since it was renamed from the European Champion Clubs' Cup to the UEFA Champions League.
The final was played between Real Madrid and Liverpool at the NSC Olimpiyskiy Stadium in Kiev, Ukraine. Real Madrid, the defending champions, beat Liverpool 3–1 to win a record-extending 13th title and their third title in a row.
As winners, Real Madrid qualified as the UEFA representative for the 2018 FIFA Club World Cup in the United Arab Emirates, and also earned the right to play against the winners of the 2017–18 UEFA Europa League, Atlético Madrid, in the 2018 UEFA Super Cup. Moreover, they would also have been automatically qualified for the 2018–19 UEFA Champions League group stage, but since they had already qualified through their league performance, the berth reserved was given to the champions of the 2017–18 Czech First League, the 11th-ranked association according to next season's access list.
2018–19 Premier LeagueThe 2018–19 Premier League is the 27th season of the Premier League, the top English professional league for association football clubs, since its establishment in 1992. The season started on 10 August 2018 and is scheduled to finish on 12 May 2019. Fixtures for the 2018–19 season were announced on 14 June 2018.Manchester City are the defending champions. Wolverhampton Wanderers, Cardiff City and Fulham joined as the promoted clubs from the 2017–18 EFL Championship. They replaced West Bromwich Albion, Swansea City and Stoke City who were relegated to the 2018–19 EFL Championship.
The season saw the occurrence of two aviation incidents involving Premier League personnel. On 27 October 2018, Leicester City owner Vichai Srivaddhanaprabha was killed in a helicopter crash outside the King Power Stadium, shortly after a 1–1 home draw against West Ham United. Almost three months later, on 21 January 2019, Cardiff City player Emiliano Sala, en route to join the club following his record signing from Nantes, died on board a Piper PA-46 Malibu aircraft that crashed off Alderney.
2018–19 UEFA Champions LeagueThe 2018–19 UEFA Champions League is the 64th season of Europe's premier club football tournament organised by UEFA, and the 27th season since it was renamed from the European Champion Clubs' Cup to the UEFA Champions League.
The final will be played at the Wanda Metropolitano in Madrid, Spain. The winners of the 2018–19 UEFA Champions League will earn the right to play against the winners of the 2018–19 UEFA Europa League in the 2019 UEFA Super Cup. They will also automatically qualify for the 2019–20 UEFA Champions League group stage, and if they have already qualified through their league performance, the berth reserved will be given to the champions of the 2018–19 Austrian Bundesliga, the 11th-ranked association according to next season's access list.For the first time, the video assistant referee (VAR) system was used in the competition from the round of 16 onward.Real Madrid were the defending champions, having won the title for three successive seasons in 2015–16, 2016–17 and 2017–18. However, they were eliminated by Ajax in the round of 16.
2018–19 UEFA Europa LeagueThe 2018–19 UEFA Europa League is the 48th season of Europe's secondary club football tournament organised by UEFA, and the 10th season since it was renamed from the UEFA Cup to the UEFA Europa League.
The final will be played at the Olympic Stadium in Baku, Azerbaijan. The winners of the 2018–19 UEFA Europa League will earn the right to play against the winners of the 2018–19 UEFA Champions League in the 2019 UEFA Super Cup. They will also automatically qualify for the 2019–20 UEFA Champions League group stage, and if they have already qualified through their league performance, the berth reserved will be given to the third-placed team of the 2018–19 Ligue 1, the 5th-ranked association according to next season's access list.For the first time, the video assistant referee (VAR) system will be used in the competition, where it will be implemented in the final.As the title holders of Europa League, Atlético Madrid qualified for the 2018–19 UEFA Champions League, although they had already qualified before the final through their league performance. They are unable to defend their title as they advanced to the Champions League knockout stage.
CONCACAF Champions LeagueThe CONCACAF Champions League is an annual continental club football competition organized by CONCACAF for the top football clubs in North America, Central America, and the Caribbean. The winner of the CONCACAF Champions League automatically qualifies for the quarter-finals of the FIFA Club World Cup. The tournament is officially known as the Scotiabank CONCACAF Champions League, since February 2015, due to sponsorship by Scotiabank. The competition has been completed 52 times through the 2016–17 event, with 54 champions due to a three-way shared title in the 1978 competition.
The tournament's current format uses a knockout format, though the tournament had a group stage prior to the 2018 tournament. Unlike its European and South American counterparts, the winners of the CONCACAF Champions League do not automatically qualify for the following season's competition.The competition was originally known as the CONCACAF Champions' Cup when it was first organized in 1962. The title has been won by 28 clubs, 17 of which have won the title more than once. Mexican clubs have accumulated the highest number of victories, with 34 titles in total. The second most successful league has been Costa Rica's Primera División with six titles in total. Mexican side Club América are the most successful club in the competition's history with seven titles, followed by fellow Mexican-side Cruz Azul with six titles. The most successful non-Mexican club is Saprissa of Costa Rica with three titles. The only four teams to successfully defend the trophy are all Mexican: América, Cruz Azul, Pachuca and Monterrey. The current champions of the competition are Guadalajara, who defeated Toronto FC in the finals.
Fibonacci numberIn mathematics, the Fibonacci numbers, commonly denoted F_{n} form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,
and
for n > 1.
One has F_{2} = 1. In some books, and particularly in old ones, F_{0}, the "0" is omitted, and the Fibonacci sequence starts with F_{1} = F_{2} = 1. The beginning of the sequence is thus:
Fibonacci numbers are strongly related to the golden ratio: Binet's formula expresses the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases.
Fibonacci numbers are named after Italian mathematician Leonardo of Pisa, later known as Fibonacci. They appear to have first arisen as early as 200 BC in work by Pingala on enumerating possible patterns of poetry formed from syllables of two lengths. In his 1202 book Liber Abaci, Fibonacci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics.
Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's bracts.
Fibonacci numbers are also closely related to Lucas numbers in that they form a complementary pair of Lucas sequences and . Lucas numbers are also intimately connected with the golden ratio.
Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0,
where the Greek letter phi ( or ) represents the golden ratio. It is an irrational number that is a solution to the quadratic equation , with a value of:
The golden ratio is also called the golden mean or golden section (Latin: sectio aurea). Other names include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, and golden number.
Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.
Some twentieth-century artists and architects, including Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.
Hypertext Transfer ProtocolThe Hypertext Transfer Protocol (HTTP) is an application protocol for distributed, collaborative, hypermedia information systems. HTTP is the foundation of data communication for the World Wide Web, where hypertext documents include hyperlinks to other resources that the user can easily access, for example by a mouse click or by tapping the screen in a web browser. HTTP was developed to facilitate hypertext and the World Wide Web.
Development of HTTP was initiated by Tim Berners-Lee at CERN in 1989. Development of HTTP standards was coordinated by the Internet Engineering Task Force (IETF) and the World Wide Web Consortium (W3C), culminating in the publication of a series of Requests for Comments (RFCs). The first definition of HTTP/1.1, the version of HTTP in common use, occurred in RFC 2068 in 1997, although this was made obsolete by RFC 2616 in 1999 and then again by the RFC 7230 family of RFCs in 2014.
A later version, the successor HTTP/2, was standardized in 2015 (and HTTP/3 is its proposed successor (Internet Draft), that builds on HTTP/2), and is now supported by major web servers and browsers over TLS using ALPN extension where TLS 1.2 or newer is required.
Ligue 1Ligue 1 , also called Ligue 1 Conforama for sponsorship reasons with Conforama, is a French professional league for men's association football clubs. At the top of the French football league system, it is the country's primary football competition. Administrated by the Ligue de Football Professionnel, Ligue 1 is contested by 20 clubs and operates on a system of promotion and relegation with Ligue 2.
Seasons run from August to May. Clubs play two matches against each of the other teams in the league – once home and once away – totalling to 38 matches over the course of the season. Most games are played on Saturdays and Sundays, with a few games played during weekday evenings. Play is regularly suspended the last weekend before Christmas for two weeks before returning in the second week of January. Ligue 1 is one of the top national leagues, currently ranked fifth in Europe behind Spain's La Liga, England's Premier League, Italy's Serie A and Germany's Bundesliga.Ligue 1 was inaugurated on 11 September 1932 under the name National before switching to Division 1 after a year of existence. The name lasted until 2002 before switching to its current name. AS Saint-Étienne is the most successful club with ten league titles in France while Olympique Lyonnais is the club that has won the most consecutive titles (seven between 2002 and 2008). With the presence of 69 seasons in Ligue 1, Olympique de Marseille hold the record for most seasons among the elite, while Paris Saint-Germain hold the league record for longevity with 45 consecutive seasons (from 1974 until at least 2019). The current champions are Paris Saint-Germain, who won their seventh title in the 2017–18 season. The league has been won on multiple occasions by foreign-based club AS Monaco, which makes the league a cross-border competition.
List of European Cup and UEFA Champions League finalsThe UEFA Champions League is a seasonal football competition established in 1955. The UEFA Champions League is open to the league champions of all UEFA (Union of European Football Associations) member associations (except Liechtenstein, which has no league competition), as well as to the clubs finishing from second to fourth position in the strongest leagues. Prior to the 1992–93 season, the tournament was named the European Cup. Originally, only the champions of their respective national league and the defending champion of the competition were allowed to participate. However, this was changed in 1997 to allow the runners-up of the stronger leagues to compete as well. In the Champions League era, the defending champion of the competition did not automatically qualify until the rules were changed in 2005 to allow title holders Liverpool to enter the competition.Teams that have won the UEFA Champions League three times in a row, or five times overall, receive a multiple-winner badge. Six teams have earned this privilege: Real Madrid, Ajax, Bayern Munich, Milan, Liverpool and Barcelona. Until 2009, clubs that had earned that badge were allowed to keep the European Champion Clubs' Cup and a new one was commissioned; since 2009, the winning team each year has received a full-size replica of the trophy, while the original is retained by UEFA.A total of 22 clubs have won the Champions League/European Cup. Real Madrid hold the record for the most victories, having won the competition 13 times, including the inaugural competition. They have also won the competition the most times in a row, winning it five times from 1956 to 1960. Juventus have been runners-up the most times, losing seven finals. Atlético Madrid is the only team to reach three finals without having won the trophy while Reims and Valencia have finished as runners-up twice without winning. Spain has provided the most champions, with 18 wins from two clubs. Italy have produced 12 winners from three clubs and England have produced 12 winners from five clubs. English teams were banned from the competition for five years following the Heysel disaster in 1985. The current champions are Real Madrid, who beat Liverpool in the 2018 final.
List of NBA championsThe National Basketball Association (NBA) (formerly Basketball Association of America (BAA) from 1946 to 1949) Finals is the championship series for the NBA and the conclusion of the NBA's postseason. All Finals have been played in a best-of-seven format, and contested between the winners of the Eastern Conference and the Western Conference (formerly Divisions before 1970), except in 1950 in which the Eastern Division champion faced the winner between the Western and Central Division champions. Prior to 1949, the playoffs were instituted a three-stage tournament where the two semifinal winners played each other in the finals. The winning team of the series receives the Larry O'Brien Championship Trophy.
The home-and-away format in the NBA Finals is in a 2–2–1–1–1 format (the team with the better regular season record plays on their home court in Games 1, 2, 5 and 7) during 1947–1948, 1950–1952, 1957–1970, 1972–1974, 1976–1977, 1979–1984, 2014–present. It was previously in a 2–3–2 format (the team with the better regular season record plays on their home court in Games 1, 2, 6 and 7) during 1949, 1953–1955, and 1985–2013, in a 1–1–1–1–1–1–1 format during 1956 and 1971 and in a 1–2–2–1–1 format during 1975 and 1978.The Eastern Conference/Division leads the Western Conference/Division in series won (38–32). The defunct Central Division won one championship. The Boston Celtics and the Minneapolis/Los Angeles Lakers alone own almost half of the titles, having won a combined 33 of 72 championships.
List of constituencies of the Lok SabhaThe Lok Sabha, the lower house of the Parliament of India, is made up of Members of Parliament (MPs). Each MP, represents a single geographic constituency. There are currently 543 constituencies.
The maximum size of the Lok Sabha as outlined in the Constitution of India is 552 members made up of up to 530 members representing people of the states of India and up to 20 members representing people from the Union Territories on the basis of their population and 2 Anglo-Indians are nominated by President.
List of countries and dependencies by populationThis is a list of countries and dependent territories by population. It includes sovereign states, inhabited dependent territories and, in some cases, constituent countries of sovereign states, with inclusion within the list being primarily based on the ISO standard ISO 3166-1. For instance, the United Kingdom is considered as a single entity, while the constituent countries of the Kingdom of the Netherlands are considered separately. In addition, this list includes certain states with limited recognition not found in ISO 3166-1.
Also given in percent is each country's population compared with the population of the world, which the United Nations estimates at 7.69 billion as of today.
Normal distribution
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.
The normal distribution is useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of samples of observations of random variables independently drawn from independent distributions converge in distribution to the normal, that is, they become normally distributed when the number of observations is sufficiently large. Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.
The normal distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student's t-, and logistic distributions).
The probability density of the normal distribution is
where
Standard deviationIn statistics, the standard deviation (SD, also represented by the lower case Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.
The standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.
A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data.
In addition to expressing the variability of a population, the standard deviation is commonly used to measure confidence in statistical conclusions. For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. This derivation of a standard deviation is often called the "standard error" of the estimate or "standard error of the mean" when referring to a mean. It is computed as the standard deviation of all the means that would be computed from that population if an infinite number of samples were drawn and a mean for each sample were computed.
It is very important to note that the standard deviation of a population and the standard error of a statistic derived from that population (such as the mean) are quite different but related (related by the inverse of the square root of the number of observations). The reported margin of error of a poll is computed from the standard error of the mean (or alternatively from the product of the standard deviation of the population and the inverse of the square root of the sample size, which is the same thing) and is typically about twice the standard deviation—the half-width of a 95 percent confidence interval.
In science, many researchers report the standard deviation of experimental data, and only effects that fall much farther than two standard deviations away from what would have been expected are considered statistically significant—normal random error or variation in the measurements is in this way distinguished from likely genuine effects or associations. The standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment.
When only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population).
USBUSB (abbreviation of Universal Serial Bus) is an industry standard that establishes specifications for cables, connectors and protocols for connection, communication and power supply between personal computers and their peripheral devices. Released in 1996, the USB standard is currently maintained by the USB Implementers Forum (USB IF). There have been three generations of USB specifications: USB 1.x, USB 2.0 and USB 3.x; the fourth called USB4 is scheduled to be published in the middle of 2019.
VarianceIn probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of (random) numbers are spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , or .
This page is based on a Wikipedia article written by authors
(here).
Text is available under the CC BY-SA 3.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.