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## Means – General Information

Some information is taken from Wikipedia.

In statistics, mean has two related meanings: $for \: series \: a_1 , a_2 , a_3 \ldots \ldots a_n$

Arithmetic mean (or just mean) is ${\sl A.M. } = \frac{1}{n} \cdot \sum \limits_{i=1}^n a_i$

Weighted arithmetic mean is ${\sl W.A.M. } = \frac{ \sum \limits_{i=1}^n w_i \cdot a_i }{ \sum \limits_{i=1}^n w_i }$

The weighted arithmetic mean is used, if one wants to combine average values from samples of the same population with different sample sizes. The weights wi represent the bounds of the partial sample. In other applications they represent a measure for the reliability of the influence upon the mean by respective values.

The geometric mean is an average that is useful for sets of positive numbers that are interpreted according to their product and not their sum (as is the case with the arithmetic mean) e.g. rates of growth. ${\sl G.M. } = \bigg( \prod \limits_{i=1}^n a_i \bigg)^{1/n}$

The harmonic mean is an average which is useful for sets of numbers which are defined in relation to some unit, for example speed (distance per unit of time). ${\sl H.M. } = n \cdot \bigg( \sum \limits_{i=1}^n {1/a_i} \bigg)^{-1}$

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1. September 24, 2011 at 15:33