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 ).

Taylor Swift

Taylor Alison Swift (born December 13, 1989) is an American singer-songwriter. Raised in Wyomissing, Pennsylvania, she moved to Nashville, Tennessee, at the age of 14 to pursue a career in country music. She signed with the independent label Big Machine Records and became the youngest songwriter ever signed by the Sony/ATV Music publishing house. The release of Swift's eponymous debut album in 2006 marked the start of her career as a country music singer. Her third single, "Our Song", made her the youngest person to single-handedly write and perform a number-one song on the Hot Country Songs chart.

Swift's second album, Fearless, was released in 2008. Buoyed by the pop crossover success of the singles "Love Story" and "You Belong with Me", Fearless became the best-selling album of 2009 in the United States. The album won four Grammy Awards, making Swift the youngest ever Album of the Year winner. Swift's third and fourth albums, 2010's Speak Now and 2012's Red, both sold more than one million copies within the first week of their U.S release. Speak Now's "Mean" won two Grammy Awards, while Red's singles "We Are Never Ever Getting Back Together" and "I Knew You Were Trouble" were successful worldwide. Swift's fifth album, the pop-focused 1989, was released in 2014 and sold more copies in its opening week than any album in the previous 12 years, making Swift the first and only act to have three albums sell more than one million copies in the opening release week. Its singles "Shake It Off", "Blank Space", and "Bad Blood" reached number one on the Billboard Hot 100. The album would go on to win three awards at the 2016 Grammys including Album of the Year making Swift the first and thus far only female artist to receive the award twice.

Jimmy Kimmel

James Christian "Jimmy" Kimmel (born November 13, 1967) is an American television host, producer, writer, comedian, voice actor, musician and radio personality. He is the host and executive producer of Jimmy Kimmel Live!, a late-night talk show that premiered on ABC in 2003. Kimmel also hosted the 64th Primetime Emmy Awards on September 23, 2012.

Prior to hosting Jimmy Kimmel Live!, he was best known as the co-host of Comedy Central's The Man Show and Win Ben Stein's Money. Kimmel has also produced such shows as Crank Yankers, Sports Show with Norm Macdonald, and The Andy Milonakis Show.

Early life

Kimmel was born in Brooklyn, New York, and grew up in the neighborhood of Mill Basin the eldest of three children of Joan (née Iacono), a homemaker, and James John Kimmel, an IBM executive.

He is, and was raised, Catholic, and as a child served as an altar boy. Kimmel's mother is of Italian ancestry; two of his paternal great-great-grandparents were German emigrants, and his family's surname was "Kümmel" several generations back. The family moved to Las Vegas, Nevada, when he was nine years old. He graduated from Ed W. Clark High School.

Jimmy Kimmel Live!

Jimmy Kimmel Live! is an American late-night talk show, created and hosted by Jimmy Kimmel, and broadcast on ABC. The nightly hour-long show made its debut on January 26, 2003, as the first program to air immediately following ABC's coverage of Super Bowl XXXVII. Jimmy Kimmel Live! is produced by Jackhole Productions in association with ABC Studios. Having aired for more than twice as long as either the The Dick Cavett Show (1969–1975) or Politically Incorrect (1997–2002), it is the longest running late-night talk show in ABC's history at 13 years and counting as of 15 February 2016.

For its first ten years, the show aired at either the Midnight or 12:05 AM timeslot before moving to 11:35 pm ET beginning on January 8, 2013 to more directly compete with The Tonight Show with Jay Leno and Late Show with David Letterman while bumping the ABC nightly news program Nightline to 12:35 am ET. Following the subsequent retirements of Leno in February 2014 and Letterman in May 2015, Kimmel is now the longest serving host in network late-night television.

Danielle Bradbery

Danielle Simone Bradbery (born July 23, 1996) is an American country singer from Cypress, Texas. She won season four of NBC's The Voice in 2013, becoming the youngest contestant to come in first place until Sawyer Fredericks of season eight. Her debut studio album, Danielle Bradbery, was released on November 25, 2013, featuring the single "The Heart of Dixie".

Early life

Bradbery was born on July 23, 1996 in League City, Texas to parents Danny Bradbery and Gloria Redden Martinez but moved to Cypress. She attended Cypress Ranch High School. Bradbery has an older sister named Monica and three younger half brothers, Drake, Drew and Collin.

Career

The Voice

At the blind auditions on March 25, 2013, Bradbery performed Taylor Swift's "Mean", prompting Adam Levine, Blake Shelton, and Usher to turn their chairs. Bradbery then chose Shelton and remained on his team. At the Battle rounds, Bradbery faced Caroline Glaser where they sang the song "Put Your Records On", Bradbery was chosen over Glaser, in the process advanced to the Knockout rounds. During the Knockouts, Bradbery sang "Jesus Take The Wheel" against Taylor Beckham in which Blake selected her to remain in the competition, sending home Beckham. During the Top 16 show, she sang "Maybe It Was Memphis" and was voted through by America into the next week. The following week, the country singer sang a rendition of Carrie Underwood's song "Wasted." During the Top 10 playoffs, Bradbery sang a rendition of "Heads Carolina, Tails California", which became the first song of the season, and only song of that round, to reach the iTunes top 10 charts.