If we add a constant (say, d) for all data values, how this will affect the geometric mean? Give an example.

zi2lalZ 2021-02-03 Answered
If we add a constant (say, d) for all data values, how this will affect the geometric mean? Give an example.
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SoosteethicU
Answered 2021-02-04 Author has 102 answers

Geometric mean of a data distribution a1,a2,a3,..,an is nth square root of product of all data points and is calculated using the below mentioned formula GM=a1a2ann=(x1x2xn)1n
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
GM=a1a2ann
=24816325
=327685
=8
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:
GM=a1a2ann
=461018345
=1468805
=10.7992
Here it is clearly shown that adding a constant to all data values increases the geometric mean of the data distribution.

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