Uses of Geometric Mean

Geometric Mean is used to compare different items, each item having multiple properties with different numerical values.
It is recurrently used for a set of numbers whose values are to be multiplied simultaneously or we are given observations which are exponential in nature, for example dataset on the increase of the human population or interest rates of a financial investment, compound annual growth rate.
In social sciences – As compared to other measures Geometric Mean works better on non-substitutable nature of statistics systematized and compared. Along with decreasing the level of substitutability between dimensions [compared] it secures that a percent decline in any vital statistics say life expectancy at birth has the same impact on the Human Development Index as a 1% decline in education. Thus, this method is most popular for natural differences as a basis for testing of achievements across the dimensions than other averages, but some values used to compute HDI are of the form (X – Xmin)/(Xnorm – Xmin) which makes the choice of the Geometric Mean less obvious than one would expect from the “Properties” section above.
Constructing index numbers.