In statistics, mean has two related meanings:

There are other statistical measures that should not be confused with averages - including 'median' and 'mode'. Other simple statistical analyses use measures of spread, such as range, interquartile range, or standard deviation. For a real-valued random variable X, the mean is the expectation of X. Note that not every probability distribution has a defined mean (or variance); see the Cauchy distribution for an example.

For a data set, the mean is the sum of the values divided by the number of values. The mean of a set of numbers x₁, x₂, ..., x_n is typically denoted by Failed to parse (Missing texvc executable; please see math/README to configure.): \bar{x} , pronounced "x bar". This mean is a type of arithmetic mean. If the data set were based on a series of observations obtained by sampling a statistical population, this mean is termed the "sample mean" (Failed to parse (Missing texvc executable; please see math/README to configure.): \bar{x} ) to distinguish it from the "population mean" (Failed to parse (Missing texvc executable; please see math/README to configure.): \mu or Failed to parse (Missing texvc executable; please see math/README to configure.): \mu _x). The mean is often quoted along with the standard deviation: the mean describes the central location of the data, and the standard deviation describes the spread. An alternative measure of dispersion is the mean deviation, equivalent to the average absolute deviation from the mean. It is less sensitive to outliers, but less mathematically tractable.

Taylor Alison Swift (born December 13, 1989) is an American singer-songwriter and occasional actress. Raised in Wyomissing, Pennsylvania, Swift moved to Nashville, Tennessee at the age of fourteen to pursue a career in country music. She signed to the independent label Big Machine Records and became the youngest songwriter ever hired by the Sony/ATV Music publishing house. The release of Swift's self-titled debut album in 2006 established her as a country music star. "Our Song", her third single, made her the youngest sole writer and singer of a number one song on the country chart. She received a Best New Artist nomination at the 50th Grammy Awards.

Swift's second album, Fearless, was released in late 2008. Buoyed by the chart success of the singles "Love Story" and "You Belong with Me", Fearless attracted a crossover audience and became the top-selling album of 2009. The record won four Grammy Awards, with Swift becoming the youngest ever Album of the Year winner. Fearless also received Album of the Year plaudits at the American Music Awards, Academy of Country Music Awards and Country Music Association Awards, making it the most awarded album in country music history. In 2010, Swift released her third album, Speak Now, which sold over one million copies in its first week. She then embarked on the 111-date Speak Now World Tour, which was attended by over 1.6 million fans and has become one of the highest-grossing concert tours of all time. The album's third single, "Mean", won two Grammy Awards for Best Country Song and Best Country Solo Performance. Swift is currently recording her fourth studio album, due for release in the fall of 2012.

Justin Drew Bieber ( /ˈbiːbər/ BEE-bər, born March 1, 1994) is a Canadian Pop/R&B singer-songwriter, musician, and actor. Bieber was discovered in 2008 by Scooter Braun, who came across Bieber's videos on YouTube and later became his manager. Braun arranged for him to meet with Usher in Atlanta, Georgia, and Bieber was soon signed to Raymond Braun Media Group (RBMG), a joint venture between Braun and Usher, and then to a recording contract with Island Records offered by L.A. Reid. Bieber's debut single, "One Time", was released in 2009 and peaked in the top twenty in Canada and charted in the top thirty in several international markets. His debut album, the seven-track EP My World, followed in November 2009, and was soon certified platinum in the United States. He became the first artist to have seven songs from a debut album chart on the Billboard Hot 100.