# Geometric Mean Formula

The geometric **mean** is a type of mean that indicates the central tendency or typical value of a set of numbers by using the product of their values. It is defined as the $n^{th}$ root of the product of $n$ numbers. You cannot calculate geometric mean from the **arithmetic mean**. Geometric mean is well defined only for positive set of real numbers. Example calculating the central frequency of a bandwidth BW=

Formula for evaluating geometric mean is as follows if we have n number of observations, then

### Solved Examples

**Question: **Find the geometric mean of 4 and 3 ?

**Solution:**

Geometric Mean = $\sqrt{4 \times 3}$ = $2\sqrt{3}$ = 3.46

**Question:**What is the geometric mean of 4, 8, 3, 9 and 17 ?

**Solution:**

Step 1: n = 5 is the total number of values. Find 1/n.

1/5 = 0.2

Step 2: Find geometric mean using the formula:

Geometric Mean = 6.81

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