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 of a projectile

In physics, assuming a flat Earth with a uniform gravity field, and no air resistance, a projectile launched with specific initial conditions will have a predictable range.

The following applies for ranges which are small compared to the size of the Earth. For longer ranges see sub-orbital spaceflight. The maximum horizontal distance traveled by the projectile

When neglecting air resistance, the range of a projectile will be

If (y₀) is taken to be zero, meaning the object is being launched on flat ground, the range of the projectile will then simplify to

Ideal projectile motion

Ideal projectile motion states that there is no air resistance and no change in gravitational acceleration. This assumption simplifies the mathematics greatly, and is a close approximation of actual projectile motion in cases where the distances travelled are small. Ideal projectile motion is also a good introduction to the topic before adding the complications of air resistance.

Ego the Living Planet

Ego the Living Planet is a fictional character appearing in American comic books published by Marvel Comics. The character first appeared in Thor #132 (Sept. 1966) and was created by writer Stan Lee and artist Jack Kirby.

Publication history

Ego the Living Planet was initially introduced in the title Thor issue #132 (Sept. 1966), and was created by writer Stan Lee and artist Jack Kirby.

Ego was created by Kirby during a phase in which he was fascinated with the universe. Ego, the alien Kree, and The Colonizers immediately followed the creation of Galactus, thus establishing Marvel Comics' own "space age mythology." As Kirby recalled in 1969, shortly after the character's debut, Ego's genesis came when:

Ego returned as a protagonist in Thor #160–161 (Jan.–Feb. 1969), and made a guest appearance in #201. His origin is explored in Thor #228.

Following appearances in Fantastic Four #234–235 (Sept.–Oct. 1981) and Rom #69 (Aug. 1985), Ego had a recurring role in Silver Surfer vol, 3 #4–22 (1987–1989). The character returned in the 1991 Thor annual and issues #448–450 (June–Aug 1992).

Select (album)

Select is the second studio album by Kim Wilde, released on May 10, 1982 via RAK label.

Overview

The first single from this album, "Cambodia", was released in November 1981 and signalled a different sound from the Wilde camp, with an electronic and synth sound different from The Enid sound of her last album. The songs were again written by Marty and Ricky Wilde and produced by Ricky Wilde. The lyrics of the songs were similar to the first album: the second single "View from a Bridge" and the album track "Wendy Sadd" seemed to be about suicide, "Chaos at the Airport" described a nightmare about flying and "Ego" was quite the opposite of a lovesong. "Can You Come Over" was recorded at the Wilde's home. The cover image was a photograph from Gered Mankowitz.

This sequel to the debut album topped the charts in a host of European countries and hit #8 in Australia — although it did not surpass the success of its predecessor. The album was certified Silver in the UK.

Critical response

Id, ego and super-ego

Id, ego, and super-ego are the three parts of the psychic apparatus defined in Sigmund Freud's structural model of the psyche; they are the three theoretical constructs in terms of whose activity and interaction our mental life is described. According to this model of the psyche, the id is the set of uncoordinated instinctual trends; the super-ego plays the critical and moralizing role; and the ego is the organized, realistic part that mediates between the desires of the id and the super-ego. The super-ego can stop one from doing certain things that one's id may want to do.

Although the model is structural and makes reference to an apparatus, the id, ego and super-ego are purely psychological concepts and do not correspond to (somatic) structures of the brain such as the kind dealt with by neuroscience. The super-ego is observable in how someone can view themself as guilty, bad, pathetic, shameful, weak, and feel compelled to do certain things. Freud (1923) in The Ego and the Id discusses "the general character of harshness and cruelty exhibited by the [ego] ideal – its dictatorial 'Thou shalt.'"