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Why does the geometric mean formula require every value to be greater than zero?
AThe root of a negative number is undefined in use
BNegative values would make the product too large
CNegative values cannot be raised to any power
DThe root of a positive number is always smaller
Answer & Solution
Correct answer: A. The root of a negative number is undefined in use
1. The geometric mean takes the nth root of a product of values.
2. A negative value can make that product negative.
3. The root of a negative number is undefined for practical use, so the formula would break down.
4. Negative returns are handled instead by converting them to positive decimal multipliers, such as 0.92 for a fall of eight percent.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.5 Geometric Mean_
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