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 root of the product of 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= 
of a bandwidth BW=
Formula for evaluating geometric mean is as follows if we have n number of observations, then
![\bar{x}_{geom}=\sqrt[n]{\prod_{i=1}^{n}x_{i}}=\sqrt[n]{x_{1}\cdot x_{2}\cdot ...\cdot x_{n}}](https://s0.wp.com/latex.php?latex=%5Cbar%7Bx%7D_%7Bgeom%7D%3D%5Csqrt%5Bn%5D%7B%5Cprod_%7Bi%3D1%7D%5E%7Bn%7Dx_%7Bi%7D%7D%3D%5Csqrt%5Bn%5D%7Bx_%7B1%7D%5Ccdot+x_%7B2%7D%5Ccdot+...%5Ccdot+x_%7Bn%7D%7D&bg=ffffff&fg=000&s=0 "\bar{x}_{geom}=\sqrt[n]{\prod_{i=1}^{n}x_{i}}=\sqrt[n]{x_{1}\cdot x_{2}\cdot ...\cdot x_{n}}")
SOLVED EXAMPLES:
Question: Find the geometric mean of 4 and 3 ?
Solution:
Geometric Mean = = = 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:
![\left [ 4*8*3*9*17 \right ]^{(0.2)}](https://s0.wp.com/latex.php?latex=%5Cleft+%5B+4%2A8%2A3%2A9%2A17+%5Cright+%5D%5E%7B%280.2%29%7D&bg=ffffff&fg=000&s=0 "\left [ 4*8*3*9*17 \right ]^{(0.2)}")
Geometric Mean = 6.81
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