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:
“Public opinion, a vulgar, impertinent, anonymous tyrant who deliberately makes life unpleasant for anyone who is not content to be the average man.”
—W.R. (William Ralph)
“A two-week-old infant cries an average of one and a half hours every day. This increases to approximately three hours per day when the child is about six weeks old. By the time children are twelve weeks old, their daily crying has decreased dramatically and averages less than one hour. This same basic pattern of crying is present among children from a wide range of cultures throughout the world. It appears to be wired into the nervous system of our species.”
—Lawrence Kutner (20th century)
“That’s one thing I like about Hollywood. The writer is there revealed in his ultimate corruption. He asks no praise, because his praise comes to him in the form of a salary check. In Hollywood the average writer is not young, not honest, not brave, and a bit overdressed. But he is darn good company, which book writers as a rule are not. He is better than what he writes. Most book writers are not as good.”
—Raymond Chandler (1888–1959)