Balanced geometric mean

In Statistiques, if one considers the data file according to:

X = { X 1, X 2,…, X N }

and associated weights:

W = { W 1, W 2,…, W N }

the balanced geometric mean is calculated in the following way:

\ bar {X} = \ left (\ prod_ {i=1} ^n x_i^ {w_i} \ right) ^ {1/\ sum_ {i=1} ^n w_i} = \ quad \ exp \ left (\ frac {\ sum_ {i=1} ^n w_i \ ln x_i} {\ sum_ {i=1} ^n w_i \ quad} \ right)

If all the weights are equal, the balanced harmonic mean is the same one as the geometric Mean .

There exist also balanced versions of the other averages. Most known being undoubtedly the weighted arithmetical mean, called simply Weighted average. Another example of weighted average is the balanced Mean harmonic.

The second expression above shows that the Logarithme balanced geometric mean is the weighted arithmetical mean of the logarithm of the values of the data file.

See too

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