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Answered question

2021-02-03

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

Answer & Explanation

SoosteethicU

Skilled2021-02-04Added 102 answers

Geometric mean of a data distribution $a_{1}, a_{2}, a_{3}, . ., a_{n}$ is $n^{t h}$ square root of product of all data points and is calculated using the below mentioned formula $G M = \sqrt[n]{a_{1} \cdot a_{2} \cdot \dots \cdot a_{n}} = {(x_{1} \cdot x_{2} \cdot \dots \cdot x_{n})}^{\frac{1}{n}}$
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
$G M = \sqrt[n]{a_{1} \cdot a_{2} \cdot \dots \cdot a_{n}}$
$= \sqrt[5]{2 \cdot 4 \cdot 8 \cdot 16 \cdot 32}$
$= \sqrt[5]{32768}$
$= 8$
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:
$G M = \sqrt[n]{a_{1} \cdot a_{2} \cdot \dots \cdot a_{n}}$
$= \sqrt[5]{4 \cdot 6 \cdot 10 \cdot 18 \cdot 34}$
$= \sqrt[5]{146880}$
$= 10.7992$
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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