Geometric Mean

#609 / Prob & Stats Easy

What is the sample geometric mean of 1, 3, 9, 27, & 81?

Expand Hint

The sample geometric mean is:

$$$\sqrt[n]{X_1X_2X_3...X_n}$$$

where $$X_1, X_2,...,X_n$$ represent the values of a random sample of $$n$$ items or observations.

Hint 2

Multiply all of the terms together, then raise the product by $$(1/n)$$ .

The sample geometric mean is:

$$$\sqrt[n]{X_1X_2X_3...X_n}$$$

where $$X_1, X_2,...,X_n$$ represent the values of a random sample of $$n$$ items or observations.

Thus,

$$$\sqrt[5]{1\cdot 3 \cdot 9\cdot 27 \cdot 81}=(59,049)^{1/5}=9$$$

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