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Encyclopedia > Weighted harmonic mean

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, ..., xn}

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, ..., 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. In mathematics, the harmonic mean is one of several methods of calculating an average. ...


Weighted versions of other means can also be calculated. Probably the best known weighted mean is the weighted arithmetic mean, usually simply called the weighted mean. Another example of a weighted mean is the weighted geometric mean. In statistics, given a set of data, X = { x1, x2, ..., xn} and corresponding weights, W = { w1, w2, ..., wn} the weighted mean is calculated as Note that if all the weights are equal, the weighted mean is the same as the arithmetic 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. ...


See also

average, summary statistics, central tendency In mathematics, there are numerous methods for calculating the average or central tendency of a list of n numbers. ... In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate as much as possible as simply as possible. ... In statistics, central tendency is an average of a set of measurements, the word average being variously construed as mean, median, or other measure of location, depending on the context. ...


References


  Results from FactBites:
 
PlanetMath: arithmetic mean (181 words)
In the special case where all the weights are equal to each other, the weighted mean equals the arithmetic mean.
See Also: geometric mean, harmonic mean, arithmetic-geometric-harmonic means inequality, general means inequality, weighted power mean, power mean, geometric distribution, root-mean-square, proof of general means inequality, proof of arithmetic-geometric-harmonic means inequality, derivation of geometric mean as the limit of the power mean, mean, a prime theorem of a convergent sequence
This is version 8 of arithmetic mean, born on 2001-10-20, modified 2006-11-11.
Mean - Encyclopedia, History, Geography and Biography (1120 words)
Sample mean is often used as an estimator of the central tendency such as the population mean.
The mean is the unique value about which the sum of squared deviations is a minimum.If you calculate the sum of squared deviations from any other measure of central tendency, it will be larger than for the mean.This explains why the standard deviation and the mean are usually cited together in statistical reports.
The mean is the arithmetic average of a set of values, or distribution; however, for skewed distributions, the mean is not necessarily the same as the middle value (median), or most likely (mode).
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