What is the geometric mean of the observation | vedclass

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(B) The geometric mean of $n$ observations $x_1, x_2, ..., x_n$ is given by $(x_1 \cdot x_2 \cdot ... \cdot x_n)^{1/n}$.
For the given observations $

Vedclass · Accepted Answer

$2^{7/2}$

Vedclass · Answer

(B) The geometric mean of $n$ observations $x_1, x_2, ..., x_n$ is given by $(x_1 \cdot x_2 \cdot ... \cdot x_n)^{1/n}$.
For the given observations $2, 4, 8, 16, 32, 64$,we can write them as powers of $2$:
$2^1, 2^2, 2^3, 2^4, 2^5, 2^6$.
Geometric mean $= (2^1 \cdot 2^2 \cdot 2^3 \cdot 2^4 \cdot 2^5 \cdot 2^6)^{1/6}$.
Sum of exponents $= 1 + 2 + 3 + 4 + 5 + 6 = 21$.
Geometric mean $= (2^{21})^{1/6} = 2^{21/6} = 2^{7/2}$.

What is the geometric mean of the observations $2, 4, 8, 16, 32, 64$?

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