Question

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

• A. $2^{\frac{5}{2}}$
• B. $2^{\frac{7}{2}}$
• C. $33$
• D. None of these

Answer 1

The correct option is B $2^{\frac{7}{2}}$

Given observations are $2,4,8,16,32,64$

$\text{G.M.}={(2\times 4\times 8\times 16\times 32\times 64)}^{\frac{1}{6}}$

$={(2\times 2^2\times 2^3\times 2^4\times 2^5\times 2^6)}^{\frac{1}{6}}$

$={\left(2^{1+2+3+4+5+6}\right)}^{\frac{1}{6}}=2^{\frac{7}{2}}$
Ans: B