First slide

Means - A.M/G.M/H.M

Question

Geometric mean of 10 observations is 8. If geometric mean of first six observations is 4, then geometric mean of last four observations is

Moderate

A

$16 \sqrt{2}$
B

$8 \sqrt{2}$
C

16
D

None of these

Solution

We are given, here geometric mean of 10 observations is 8 and geometric mean of first six observations is 4, then we have to find the geometric mean of last four observations. Let G be the GM of last four observations. $∴$ By using grouped geometric mean,
$\begin{array}{ll} i.e., & 8^{10} = 4^{6} \times G^{4} \\ \Rightarrow & G^{4} = \frac{8^{10}}{4^{6}} = \frac{2^{30}}{2^{12}} = 2^{18} \\ \Rightarrow & G = 2^{18 / 4} = 2^{4} \sqrt{2} = 16 \sqrt{2} \end{array}$

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