If the observations 2,4,8 and 16 occur 8, 6,4 and 2 times respectively, then the geometric mean of the observations is

A
8
B
$4 \sqrt{2}$
C
4
D
None of these

Solution:

$∵ we know$

Geometric mean $\begin{array}{l} = \sqrt[n]{x_{1} \times x_{2} \times \dots \times x_{n}} \\ = \sqrt[20]{2^{8} \times 4^{6} \times 8^{4} \times 16^{2}} \\ = \sqrt[20]{2^{8} \times 2^{12} \times 2^{12} \times 2^{8}} \\ = \sqrt[20]{2^{40}} = 2^{\frac{40}{20}} = 2^{2} = 4 \end{array}$

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