Two possible observations have arithmetic mean 3 and geometric mean 22.If each observation is multiplied by 2, then harmonic mean will be

Two possible observations have arithmetic mean 3 and geometric mean $2 \sqrt{2}$ .If each observation is multiplied by 2, then harmonic mean will be

A
$\frac{16}{3}$
B
$\frac{8}{3}$
C
12
D
None of these

Solution:

Since, we know that

$\begin{aligned} (GM)^{2} = AM \times HM \\ (2 \sqrt{2})^{2} = 3 \times HM \\ \Rightarrow HM = \frac{8}{3} \end{aligned}$

Also, given here that, if each observation is multiplied
by 2, then $HM = \frac{8}{3} \times 2 = \frac{16}{3}$

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