Question

The Geometric Mean (GM) for
the series 1, 3, 9 is​

Answer 1

Answer:

First we multiply them: 2 × 18 = 36

Then (as there are two numbers) take the square root: √36 = 6

In one line:

Geometric Mean of 2 and 18 = √(2 × 18) = 6

It is like the area is the same!

geometric mean 2x18 = 6x6

Answer 2

Answer:

The Geometric Mean of 1, 3 and 9 is 3

Step-by-step explanation:

Geometric mean is a type of mean which is used to find value of the central tendency of any given series by taking nth root of the values by multiplying the numbers and finding the product of the numbers.

In other words, it could be simply defined as the nth root of the product of n numbers given in the series. So it is done by multiplying all the given numbers and taking the nth root of the values. Where, n is the total number of data in the series.

The formula for Geometric Mean (GM) is given by,

Geometric Mean = $\sqrt[n]{x_{1} *x_{2}* x_{3} *x_{4} *x_{5}...x_{n} }$

It can also be expressed as,

GM = $(x_{1}* x_{2}* x_{3}* x_{4}* x_{5}*... x_{n} )^{1/n}$

So for the given series 1, 3, 9 the geometric mean is given by

Geometric Mean = $( 1 * 3 * 9)^{1/3}$

                            =  ∛27

                            =  3

Geometric Mean = 3

Therefore, the Geometric Mean of the series 1, 3, 9 is 3

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