# Average Value of Mean Calculator

Find the geometric average mean value of the given numbers.

The geometric mean is a special type of average for a set of n numbers by using the product of their values (multiply them all together) and then take nth root.

**For example :**

Geometric mean for two numbers, multiply them and take square root, geometric mean three numbers, multiply all together and take cube root.

Hence the ** Geometric Mean Formula **is as follows

Geometric Mean = {(X_{1})(X_{2})(X_{3})........(X_{n})}^{1/n}

## Geometric Mean Properties

The Geometric Mean for the given data set is always less than the arithmetic mean for the data set.

If each object in the data set is substituted by the Geometric Mean, then the product of the objects remains unchanged.

The ratio of the corresponding observations of the Geometric Mean in two series is equal to the ratio of their geometric means.

The products of the corresponding items of the Geometric Mean in two series are equal to the product of their geometric mean.

### Geometric Mean -Application

Geometric mean has many advantages and used in many applications as follows:

Geometric Mean may be used in stock indexes. and used to calculate the annual return on the portfolio.

Geometric Mean may be used in finance to find the average growth rates / compounded annual growth rate.

Geometric Mean may be used in studies like cell division and bacterial growth etc.