In statistics, given a set of data, Statistics is a type of data analysis which practice includes the planning, summarizing, and interpreting of observations of a system possibly followed by predicting or forecasting of future events based on a mathematical model of the system being observed. ...

X = { x₁, x₂, ..., x_n}

and corresponding weights, A weight function is a mathematical device used when performing a sum, integral, or average in order to give some elements more of a weight than others. ...

W = { w₁, w₂, ..., w_n}

the weighted mean is calculated as

Note that if all the weights are equal, the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counter-intuitive properties, as captured for instance in Simpson's paradox. In mathematics and statistics, the arithmetic mean of a set of numbers is the sum of all the members of the set divided by the number of items in the set. ... Simpsons paradox (or the Yule-Simpson effect) is a statistical paradox described by E. H. Simpson in 1951 and G. U. Yule in 1903, in which the successes of several groups seem to be reversed when the groups are combined. ...

Weighted versions of other means can also be calculated. Examples of such weighted means include the weighted geometric mean and the weighted harmonic mean. In statistics, given a set of data, X = { x1, x2, ..., xn} and corresponding weights, W = { w1, w2, ..., wn} the weighted geometric mean is calculated as Note that if all the weights are equal, the weighted geometric mean is the same as the geometric mean. ... In statistics, given a set of data, X = { x1, x2, ..., xn} and corresponding weights, W = { w1, w2, ..., wn} the weighted harmonic mean is calculated as Note that if all the weights are equal, the weighted harmonic mean is the same as the harmonic mean. ...

See also

• average
• summary statistics
• central tendency