Why is a geometric mean rather than an arithmetic mean used to summarize annual rates of price change?
Correct Answer
A) It reflects the compounding between periods
Why this is correct: The geometric mean is used for rates of change because it accounts for the compounding effect over multiple periods. If you have annual growth rates, the geometric mean correctly calculates the single rate that, if applied each year, would produce the same total growth as the actual varying rates. Why the other choices are wrong: The geometric mean is not always larger; it is typically smaller than or equal to the arithmetic mean when rates vary. It does not specifically remove outliers; other measures do that. It does not require fewer observations to compute. Exam tip: Use the geometric mean for multiplicative data like growth rates. Use the arithmetic mean for additive data.
Why This Is the Correct Answer
Why this is correct: The geometric mean is used for rates of change because it accounts for the compounding effect over multiple periods. If you have annual growth rates, the geometric mean correctly calculates the single rate that, if applied each year, would produce the same total growth as the actual varying rates. Why the other choices are wrong: The geometric mean is not always larger; it is typically smaller than or equal to the arithmetic mean when rates vary. It does not specifically remove outliers; other measures do that. It does not require fewer observations to compute. Exam tip: Use the geometric mean for multiplicative data like growth rates. Use the arithmetic mean for additive data.
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