# The geometric mean of a set of observations is computed as 10. The geometric mean obtained when each observations xi is replaced by $\rm 3x_i^4$ is

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The geometric mean of a set of observations is computed as 10. The geometric mean obtained when each observations xi is replaced by $\rm 3x_i^4$ is
1. 810
2. 900
3. 30000
4. 81000

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Correct Answer - Option 3 : 30000

Concept:

If GM of series xi = a, then

• GM of λxi = λa
• GM of $\rm {x_i}^n$ = an

Calculation:

Given GM of xi = 10

Then GM of $\rm {x_i}^4$ = 104 = 10000

Now GM of $\rm 3{x_i}^4$ = 3 × 10000 = 30000