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Why does the arithmetic mean of a series of annual growth rates overstate the true average growth?
AIt is additive and ignores interest on the interest
BIt is additive and gives outliers too little weight
CIt divides by n rather than by n minus one
DIt uses the product of the rates, not the sum
Answer & Solution
Correct answer: A. It is additive and ignores interest on the interest
1. Growth over several periods compounds, so each period builds on the value left by the last.
2. The arithmetic mean simply adds the rates and divides, which treats every period as starting afresh.
3. Because it ignores the interest earned on earlier interest, it reports a higher average than the investment actually delivered.
4. The geometric mean multiplies the multipliers instead, so it carries the compounding through.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.5 Geometric Mean_
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