The geometric mean takes a set of positive numbers, multiplies them together, and then takes the root based on how many numbers there are. It proves particularly useful for rates and proportions, as it tends to reveal more about the way the values interrelate than an arithmetic mean would. It has the added advantage of reducing the effect of extremely high or low numbers so that a more accurate average may result in those circumstances.

Definition: The geometric mean is the measure of central tendency which is very helpful in working with sets of positive numbers. It is defined as the n th roots of the product of n values.

Formula

The formula for the geometric mean (GM) of a set of positive numbers

Notation In GM Formula:

Example Question Applying Geometric Mean Formula

Question 1: Compute the geometric mean of 4 and 3.

Solution: Applying G.M. formula, the G.M. of 4 and 3 will be:

Geometric Mean will be √(4×3)

= 2√3

So, GM = 3.46

Question 2: Compute the geometric mean of 4, 8, 3, 9 and 17?

Solution:

Step 1: n = 5 is the number of values. Now, calculate 1/n.

1/5 = 0.2.

Step 2: Calculate geometric mean using the following formula:

(4 × 8 × 3 × 9 × 17)0.2

Geometric Mean = 6.814

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