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

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

1. A

8

2. B

$4\sqrt{2}$

3. C

4

4. D

None of these

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