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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

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