In mathematics, an average is a measure of the "middle" or "typical" value of a data set. It is thus a measure of central tendency.
In the most common case, the data set is a list of numbers. The average of a list of numbers is a single number intended to typify the numbers in the list. If all the numbers in the list are the same, then this number should be used. If the numbers are not the same, the average is calculated by combining the numbers from the list in a specific way and computing a single number as being the average of the list.
Many different descriptive statistics can be chosen as a measure of the central tendency of the data items. These include the arithmetic mean, the median, and the mode. Other statistics, such as the standard deviation and the range, are called measures of spread and describe how spread out the data is.
The most common statistic is the arithmetic mean, but depending on the nature of the data other types of central tendency may be more appropriate. For example, the median is used most often when the distribution of the values is skewed with a small number of very high or low values, as seen with house prices or incomes. It is also used when extreme values are likely to be anomalous or less reliable than the other values (e.g. as a result of measurement error), because the median takes less account of extreme values than the mean does.
Read more about Average: Calculation, Types, Solutions To Variational Problems, Miscellaneous Types, In Data Streams, Average Values of Functions, Etymology
Famous quotes containing the word average:
“The average American is a good sport, plays by the rules. But this war is no game. And no secret agent is a hero or a good sport—that is, no living agent.”
—John Monks, Jr., U.S. screenwriter, Sy Bartlett, and Henry Hathaway. Robert Sharkey (James Cagney)
“Three million of such stones would be needed before the work was done. Three million stones of an average weight of 5,000 pounds, every stone cut precisely to fit into its destined place in the great pyramid. From the quarries they pulled the stones across the desert to the banks of the Nile. Never in the history of the world had so great a task been performed. Their faith gave them strength, and their joy gave them song.”
—William Faulkner (1897–1962)
“... there is nothing more irritating to a feminist than the average “Woman’s Page” of a newspaper, with its out-dated assumption that all women have a common trade interest in the household arts, and a common leisure interest in clothes and the doings of “high society.” Women’s interests to-day are as wide as the world.”
—Crystal Eastman (1881–1928)