Statistics
 Central Tendency Measures Measures of Dispersion Measures of skewness and kurtosis
Geometric Mean.

The geometric mean of a set of n values of a variable is the n th root of their product. If a variable x assumes n values , then its geometric mean, denoted by is

For a frequency distribution, , where

Properties:

• If the given values of a variable are all equal, then the geometric mean will be equal to their common value.
• The logarithm of the geometric mean of a set of values of a variable is the aritmetic mean of their logarithms.
• If y is a function of a variable x in the form y=ax, then the geometric mean of y is related to that of x in the similar form.
• The geometric mean of the ratio of two variables is the ratio of their geometric means.
• If there are two sets of values of a variable x, consisting of n1 and n2 values, and G1 and G2 are their respective geometric means, then the geometric mean, G, of the combined set is given by
• If a variable x chages over time t exponentially, then the value of the variable at the mid-point of an interval (t1,t2) i.e. at is the geometric mean of its values at t1 and t2.
• No es útil si algún valor es nulo.
• No es posible su cálculo cuando hay un número par de datos y el radicando es negativo.

• The geometric mean is ridigly defined.
• The geometric mean is directly based on all the observations.
• Generally, the presence of a few extremely small or large values has no considerable effect on geometric mean.