Mean

In mathematics, mean has several different definitions depending on the context.

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together, giving . An analogous formula applies to the case of a continuous probability distribution. Not every probability distribution has a defined mean; see the Cauchy distribution for an example. Moreover, for some distributions the mean is infinite: for example, when the probability of the value is for n = 1, 2, 3, ....

For a data set, the terms arithmetic mean, mathematical expectation, and sometimes average are used synonymously to refer to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x₁, x₂, ..., x_n is typically denoted by , pronounced "x bar". If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is termed the sample mean (denoted ) to distinguish it from the population mean (denoted or ).

Statistics

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all persons living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.

When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.

Denver Dalley

Denver Collin Dalley is an American singer-songwriter based in Omaha, Nebraska. He is best known for his collaboration with Bright Eyes frontman Conor Oberst in Desaparecidos, and has been involved in various other musical projects, including Statistics, Intramural, and Two of Cups.

Career

Desaparecidos

Dalley collaborated with childhood friend Conor Oberst as main songwriter of the politically charged indie rock band Desaparecidos. The band released Read Music/Speak Spanish on Omaha-based Saddle Creek Records before going on hiatus in 2003. They reunited in 2010, performing at the Concert for Equality in Omaha on July 31, and again on July 31, 2012 at Omaha's Maha Music Festival.

Statistics

In 2003, following the temporary caesura of Desaparecidos, Dalley formed Statistics, an electronic-tinged solo project, and signed onto the Jade Tree Records label. After releasing a self-titled extended play in 2003 and two studio albums titled Leave Your Name and Often Lie in 2004 and 2005, respectively, Dalley chose to focus on other projects, effectively putting Statistics on hiatus. However, in 2013, eight years after Often Lie, Dalley released a new studio album titled Peninsula on Afternoon Records, featuring a collaboration with Minnesota-based singer-songwriter Sean Tillman (a.k.a. Har Mar Superstar). Dalley hopes to create visuals in the form of music videos for songs in Peninsula, something that he has never done in his prior musical ventures.

Statistics (disambiguation)

Statistics is a mathematical science pertaining to the collection, analysis, interpretation, and presentation of data.

Statistic may also refer to:

Mean (song)

"Mean" is a song written and recorded by American country pop singer-songwriter Taylor Swift for her third studio album, Speak Now (2010). Produced by Swift alongside Nathan Chapman, the song was sent to country radio in the United States on March 13, 2011, as the third single from Speak Now. "Mean" garnered mixed to positive reviews from critics for its lyrical detail and profound country sound. The song received commercial success in the United States and Canada, debuting at number 11 on the Billboard Hot 100 and number ten on the Canadian Hot 100. The song also appeared on the Australian Singles Chart at number 45.

The song's accompanying music video was directed by Declan Whitebloom, who developed the concept together with Swift. It received mixed reviews from critics who perceived ambivalent messages in the video, despite the prevalent self-empowerment and anti-bullying themes. "Mean" was performed for the first time by Swift at the 46th Annual Academy of Country Music Awards on April 3, 2011. The song won the Grammy Awards for Best Country Song and Best Country Solo Performance at the 54th Grammy Awards.Rolling Stone Magazine ranked Mean as #24 on their list of the 100 greatest country songs of all time. Taylor Swift was tied up in the music video for mean.

Arithmetic mean

In mathematics and statistics, the arithmetic mean (pronunciation: /ˌærɪθˈmɛtɪk ˈmiːn/, stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection. The collection is often a set of results of an experiment, or a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean and the harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.

While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influenced by outliers (values that are very much larger or smaller than most of the values). Notably, for skewed distributions, such as the distribution of income for which a few people's incomes are substantially greater than most people's, the arithmetic mean may not accord with one's notion of "middle", and robust statistics, such as the median, may be a better description of central tendency.

Mean (album)

Mean is the fifth and final album by the California-based hard rock band Montrose and released in 1987. It has much more of a glam metal sound than previous Montrose albums.

According to Ronnie Montrose, singer Johnny Edwards and drummer James Kottak were still officially in the band Buster Brown at the time of the recording of Mean. They later played together in the first line-up of the band Wild Horses.

Guitarist Ronnie Montrose and bassist Glenn Letsch played together in the band Gamma both before and after this album.

It features the song "M for Machine" which was written as a potential song for the 1987 American cyberpunk action film RoboCop, directed by Paul Verhoeven.

Drummer James Kottak would go on to join the original line-up of hard rock/glam metal band Kingdom Come, remaining with that band during their most commercially successful period, prior to reconnecting with Edwards in Wild Horses. After leaving Wild Horses, Edwards became the frontman for Foreigner on their 1991 album, Unusual Heat.