# Geometric Mean definiton, formula and applications

The Geometric mean is a special types of average where we calculate the root of the product of a value of a set of observations. It is usually used to define various types of growth rates such as population growth, interest rates etc.

### Formula of geometric mean

By definition, the formula is as below,

G.M = Where, G.M=geometric mean

n=number of observations

### Mathematical example

What is the geometric mean of 2, 3, and 6?
First, multiply the numbers together and then take the cubed root (because there are three numbers) = (2*3*6)1/3 = 3.30

Note: The power of (1/3) is the same as the cubed root 3√. To convert a nth root to this notation, just change the denominator in the fraction to whatever “n” you have. So,

• 5th root = to the (1/5) power
• 12th root = to the (1/12) power
• 99th root = to the (1/99) power.…….

### The situation where we use geometric mean

The geometric mean is the most appropriate measure of location when,

It is appropriate for averaging the ratios of change, for average of proportions, etc.

There are some merits as following,

• Geometric mean is least affected by extreme values.
• It is based on all observations of the set.
• It is suitable for further algebraic treatment.

There are some demerits as following,

• Geometric mean calculation is somewhat complicated.
• It cannot be calculated if any of the values in the set is zero.
• If any one or more values are negative, either it will not be calculable, or an absurd value will be obtained.

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