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, ..., X_n with cumulative distribution function G(x) and probability density function g(x) the range of the X_i 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.

Xenosaga

Xenosaga (ゼノサーガ, Zenosāga) is a series of science fiction video games developed by Monolith Soft and published by Bandai Namco. Xenosaga's main story is in the form of a trilogy of PlayStation 2 video games. There have been three spin-off games and an anime adaptation. The Xenosaga series serves as a spiritual successor to the game Xenogears, which was released in 1998 for the PlayStation by Square. The creator of both Xenogears and Xenosaga is Tetsuya Takahashi, who left Square in 1998 along with Hirohide Sugiura. Using funds from Namco, they started MonolithSoft and the Xenosaga project.

The first game in the trilogy, Episode I: Der Wille zur Macht was released in February 2002 in Japan, and in February 2003 in North America. Xenosaga Freaks, a lighthearted game with a playable demo for Episode II, was released in April 2004 in Japan, but was not released elsewhere. Episode II: Jenseits von Gut und Böse was released in June 2004 in Japan and February 2005 in North America. Xenosaga: The Animation, an anime based on Episode I, premiered on TV Asahi in Japan on January 5, 2005. Xenosaga Pied Piper, a three chapter-long cellphone-based game depicting the history of cyborg "Ziggurat 8" 100 years before the start of Episode I, was released in Japan in July 2004. Released on July 6, 2006, Episode III: Also sprach Zarathustra is the final title in the Xenosaga series; six episodes were originally projected, but by the time Episode III was released, Namco had already established that it would be the last entry, effectively halving the series. A retelling of the first two episodes titled Xenosaga I & II was released on the Nintendo DS in March 2006 in Japan.

Transformers (toy line)

The Transformers (トランスフォーマー, Toransufomā) is a line of toys produced by the Japanese company Takara (now known as Takara Tomy) and American toy company Hasbro. The Transformers toyline was created from toy molds mostly produced by Japanese company Takara in the toylines Diaclone and Microman. Other toy molds from other companies such as Bandai were used as well. In 1984, Hasbro bought the distribution rights to the molds and rebranded them as the Transformers for distribution in North America. Hasbro would go on to buy the entire toy line from Takara, giving them sole ownership of the Transformers toy-line, branding rights, and copyrights, while in exchange, Takara was given the rights to produce the toys and the rights to distribute them in the Japanese market. The premise behind the Transformers toyline is that an individual toy's parts can be shifted about to change it from a vehicle, a device, or an animal, to a robot action figure and back again. The taglines "More Than Meets The Eye" and "Robots In Disguise" reflect this ability.

Hammer (disambiguation)

A hammer is a type of tool.

Hammer may also refer to:

People

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Germany

In the United States

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Entertainment

In film