Range (statistics)
In arithmetic, the range of a set of data is the difference between the largest and smallest values.
However, in descriptive statistics, this concept of range has a more complex meaning. The range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. It is measured in the same units as the data. Since it only depends on two of the observations, it is most useful in representing the dispersion of small data sets.
Independent identically distributed continuous random variables
For n independent and identically distributed continuous random variables X1, X2, ..., Xn with cumulative distribution function G(x) and probability density function g(x) the range of the Xi is the range of a sample of size n from a population with distribution function G(x).
Distribution
The range has cumulative distribution function
Gumbel notes that the "beauty of this formula is completely marred by the facts that, in general, we cannot express G(x + t) by G(x), and that the numerical integration is lengthy and tiresome."
Range (music)
In music, the range of a musical instrument is the distance from the lowest to the highest pitch it can play. For a singing voice, the equivalent is vocal range. The range of a musical part is the distance between its lowest and highest note.
The terms sounding range, written range, designated range, duration range and dynamic range have specific meanings.
The sounding range refers to the pitches produced by an instrument, while the written range refers to the compass (span) of notes written in the sheet music, where the part is sometimes transposed for convenience. A piccolo, for example, typically has a sounding range one octave higher than its written range. The designated range is the set of notes the player should or can achieve while playing. All instruments have a designated range, and all pitched instruments have a playing range. Timbre, dynamics, and duration ranges are interrelated and one may achieve registral range at the expense of timbre. The designated range is thus the range in which a player is expected to have comfortable control of all aspects.
Range (particle radiation)
In passing through matter, charged particles ionize and thus lose energy in many steps, until their energy is (almost) zero. The distance to this point is called the range of the particle. The range depends on the type of particle, on its initial energy and on the material through which it passes.
For example, if the ionising particle passing through the material is a positive ion like an alpha particle or proton, it will collide with atomic electrons in the material via Coulombic interaction. Since the mass of the proton or alpha particle is much greater than that of the electron, there will be no significant deviation from the radiation's incident path and very little kinetic energy will be lost in each collision. As such, it will take many successive collisions for such heavy ionising radiation to come to a halt within the stopping medium or material. Maximum energy loss will take place in a head-on collision with an electron.
Since large angle scattering is rare for positive ions, a range may be well defined for that radiation, depending on its energy and charge, as well as the ionisation energy of the stopping medium. Since the nature of such interactions is statistical, the number of collisions required to bring a radiation particle to rest within the medium will vary slightly with each particle (i.e., some may travel further and undergo less collisions than others). Hence, there will be a small variation in the range, known as straggling.
Unbreakable (horse)
Unbreakable (1935–1952) was an American-bred, British-trained Thoroughbred racehorse and sire. He was successful on the racecourse, but some way below the best of his generation. His best wins came in the Richmond Stakes at Goodwood as a two-year-old and in the Victoria Cup Handicap two years later. After his retirement from racing he became a highly successful breeding stallion: through his grandson Native Dancer he appears in the pedigrees of most modern Thoroughbreds.
Background
Unbreakable was a black horse bred in the United States by his owner, Joseph E. Widener. He was sent to race in England, where he was trained by Cecil Boyd-Rochfort. The colt was sired by the British-bred stallion Sickle out of the French mare Blue Glass, making him a half-brother to the Belmont Stakes winner Hurryoff.
Racing career
As a two-year-old, Unbreakable won three races including the Richmond Stakes at Goodwood in July. In the following year he competed at the highest level, finishing fifth to Pasch in the 2000 Guineas and eighth behind Bois Roussel in the Epsom Derby.
Unbreakable (TV series)
Unbreakable is a reality television series presented by Explorer Benedict Allen on UK's Channel 5, where eight volunteers undergo an onslaught of physical and mental pressure in a bid to be declared unbreakable.
Filmed across four continents, Unbreakables takes eight super-fit members of the public on a punishing global trail to undergo a series of brutal challenges.
From the Norwegian arctic to the Sahara Desert, the volunteers will learn to survive in the world's harshest environments and endure some of the toughest military training around. They will be bossed and cajoled by physical trainers and survival experts as they bid to outdo and outlast each other.
Contestants
Episodes
Episode 1
The jungle of Guyana. They're spurred on by Mark Billingham, a jungle warfare instructor who served with special forces. They also face challenges inspired by a tribe of former cannibals.
Episode 2
Norwegian School of Winter Warfare in Norway. They are placed in the vicinity of a TNT explosion and forced to jump into an ice hole while still wearing their skis. During the nights they were required to dig a snow holes and sleep in them.
Unbreakable (Fireflight album)
Unbreakable is the third full-length studio album released by Christian rock band Fireflight, but second full-length to be released on Flicker Records. The album was released on March 4, 2008 on Flicker Records.
Background
Unbreakable was recorded in September and October 2007.Lead vocalist Dawn Michele said that the recording process was "one of the most hectic times in our lives because we had about six years to write the first album and about six months to write the second one".
The album was produced by Rob Hawkins.
Release and promotion
The album's title track "Unbreakable" was officially released to radio in December 2007. The song was featured on an episode of NBC's Bionic Woman. A music video for "Unbreakable" made its premiere on March 29, 2008.
The album's second radio single, "The Hunger", was released in mid-2008. As of June 2010, the album sold about 100,000 copies.
Style and lyrical themes
The band's female-fronted hard rock sound has been compared to Paramore and Evanescence, and Dawn Michele's vocals on Unbreakable have been described as "riveting".Allmusic reviewer Jared Johnson labeled certain tracks as "pulsating rockers", such as the singles "Unbreakable" and "The Hunger"; he described the album's lyrics to be "victorious as a refuge for listeners struggling with loneliness, discouragement, and isolation."Guitarist Justin Cox said, "we push it as heavy as we can without being metal".
Podcasts:
