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.

Illusion

An illusion is a distortion of the senses, revealing how the brain normally organizes and interprets sensory stimulation. Though illusions distort reality, they are generally shared by most people. Illusions may occur with any of the human senses, but visual illusions (optical illusions), are the most well-known and understood. The emphasis on visual illusions occurs because vision often dominates the other senses. For example, individuals watching a ventriloquist will perceive the voice is coming from the dummy since they are able to see the dummy mouth the words. Some illusions are based on general assumptions the brain makes during perception. These assumptions are made using organizational principles (e.g., Gestalt theory), an individual's capacity for depth perception and motion perception, and perceptual constancy. Other illusions occur because of biological sensory structures within the human body or conditions outside of the body within one’s physical environment.

The term illusion refers to a specific form of sensory distortion. Unlike a hallucination, which is a distortion in the absence of a stimulus, an illusion describes a misinterpretation of a true sensation. For example, hearing voices regardless of the environment would be a hallucination, whereas hearing voices in the sound of running water (or other auditory source) would be an illusion.

Faith Hill

Faith Hill (born Audrey Faith Perry; September 21, 1967) is an American country pop singer and occasional actress. She is one of the most successful country artists of all time, having sold more than 40 million albums worldwide. Hill is married to country singer Tim McGraw, with whom she has recorded several duets.

Hill's first two albums, Take Me as I Am (1993) and It Matters to Me (1995), were major successes and placed a combined three number ones on Billboard's country charts. She then achieved mainstream and crossover success with her next two albums, Faith (1998) and Breathe (1999). Faith spawned her first international hit, "This Kiss", and went multi-platinum in various countries. Breathe became her best-selling album to date and one of the best-selling country albums of all time, with the huge crossover success of the songs "Breathe" and "The Way You Love Me". It had massive sales worldwide and earned Hill three Grammy Awards, including Best Country Album.

In 2001, she recorded "There You'll Be" for the Pearl Harbor soundtrack and it became an international hit and her best-selling single in Europe. Hill's next two albums, Cry (2002) and Fireflies (2005), were both commercial successes and kept her mainstream popularity; the former spawned another crossover single, "Cry", which won Hill a Grammy Award, and the latter produced the hit singles "Mississippi Girl" and "Like We Never Loved at All", which earned her another Grammy Award.

The Elder Scrolls

The Elder Scrolls is a series of action role-playing open world fantasy video games primarily developed by Bethesda Game Studios and published by Bethesda Softworks. The series is known for its elaborate and richly detailed open worlds and its focus on free-form gameplay. Morrowind, Oblivion, and Skyrim all won Game of the Year awards from multiple outlets. The series has sold more than 40 million copies worldwide.

Development history

Before The Elder Scrolls

Prior to working on The Elder Scrolls series, Bethesda had worked predominantly with sports and action games. In the six years from its founding to Arena's 1994 release, Bethesda had released ten games, six of them sports games, with such titles as Hockey League Simulator, NCAA Basketball: Road to the Final Four ('91/'92 Edition), and Wayne Gretzky Hockey, and the remaining four adaptations from other media, primarily the Terminator series. Bethesda's course changed abruptly when it began its first action role-playing venture. Designer Ted Peterson recalls: "I remember talking to the guys at Sir-Tech who were doing Wizardry VII: Crusaders of the Dark Savant at the time, and them literally laughing at us for thinking we could do it." Ted Peterson worked alongside Vijay Lakshman as one of the initial designers of what was then simply Arena, a "medieval-style gladiator game."