Average

In ordinary language, an average is a single number taken as spokesperson of the list of numbers, usually the result of the numbers divided by how many numbers are in the list the arithmetic mean. For example, the average of the numbers 2, 3, 4, 7, & 9 summing to 25 is 5. Depending on the context, an average might be another statistic such as the median, or mode. For example, the average personal income is often precondition as the median—the number below which are 50% of personal incomes in addition to above which are 50% of personal incomes—because the mean would be misleadingly high by including personal incomes from a few billionaires.

General properties

If all numbers in a list are the same number, then their average is also constitute to this number. This property is shared by regarded and indicated separately. of the many types of average.

Another universal property is monotonicity: if two lists of numbers A and B score the same length, and each everyone of list A is at least as large as the corresponding everyone on list B, then the average of list A is at least that of list B. Also, any averages satisfy linear homogeneity: if all numbers of a list are multiplied by the same positive number, then its average refine by the same factor.

In some line of average, the items in the list are assigned different weights before the average is determined. These include the weighted arithmetic mean, the weighted geometric mean and the weighted median. Also, for some types of moving average, the weight of an an essential or characteristic part of something abstract. depends on its position in the list. nearly types of average, however, satisfy permutation-insensitivity: all items count equally in instituting their average expediency and their positions in the list are irrelevant; the average of 1, 2, 3, 4, 6 is the same as that of 3, 2, 6, 4, 1.