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.
Famous quotes containing the word average:
“The average Hollywood film stars ambition is to be admired by an American, courted by an Italian, married to an Englishman and have a French boyfriend.”
—Katharine Hepburn (b. 1909)
“Does there, I wonder, exist a being who has read all, or approximately all, that the person of average culture is supposed to have read, and that not to have read is a social sin? If such a being does exist, surely he is an old, a very old man.”
—Arnold Bennett (18671931)
“Here is a golden Rule.... Write legibly. The average temper of the human race would be perceptibly sweetened, if everybody obeyed this Rule!”
—Lewis Carroll [Charles Lutwidge Dodgson] (18321898)