Discussion
When an observation in the data is zero, then its geometric mean is :
Answer: B
The geometric mean is zero.
The geometric mean of n values is the nth root of their product. If any observation is zero, the product is zero, and so is its root:
\[ G = \sqrt[n]{x_1 x_2 \cdots 0 \cdots x_n} = 0 \]
The result is neither negative nor positive. Because a zero makes the measure uninformative, the geometric mean is said to be unsuitable for such data, which is why 'cannot be calculated' is a tempting distractor, but the value itself is zero.
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