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:
“... to be successful a person must attempt but one reform. By urging two, both are injured, as the average mind can grasp and assimilate but one idea at a time.”
—Susan B. Anthony (18201906)
“And since the average lifetimethe relative longevityis far greater for memories of poetic sensations than for those of heartbreaks, since the very long time that the grief I felt then because of Gilbert, it has been outlived by the pleasure I feel, whenever I wish to read, as in a sort of sundial, the minutes between twelve fifteen and one oclock, in the month of May, upon remembering myself chatting ... with Madame Swann under the reflection of a cradle of wisteria.”
—Marcel Proust (18711922)
“The average educated man in America has about as much knowledge of what a political idea is as he has of the principles of counterpoint. Each is a thing used in politics or music which those fellows who practise politics or music manipulate somehow. Show him one and he will deny that it is politics at all. It must be corrupt or he will not recognize it. He has only seen dried figs. He has only thought dried thoughts. A live thought or a real idea is against the rules of his mind.”
—John Jay Chapman (18621933)