Geometric mean of a data distribution
When a constant d is added to all data values, the product of all numbers will increase, so the geometric mean of the data distribution also increases by adding a constant to all values.
Let us consider an example data distribution 2,4,8,16,32
The geometric mean is calculated as shown below
If we add a constant 2 to all data points then the data distribution will be 4 ,6 ,10, 18, 34. The geometric mean is calculated as shown below:
Here it is clearly shown that adding a constant to all data values increases the geometric mean of the data distribution.