Chapter 11.1, Problem 38E

To determine

To compare arithmetic mean to the geometric mean of n numbers.

Answer to Problem 38E

• An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers.
• The geometric mean for a series of numbers is calculated by taking the product of these numbers and raising it to the inverse of the length of the series.

Explanation of Solution

Given information: Geometric Mean = $\sqrt[n]{a_1\cdot a_2\cdot a_3\cdot \mathrm{....}\cdot a_n}$ .

Calculation:

The geometric mean differs from the arithmetic average, or arithmetic mean, in how it is calculated because it takes into account the compounding that occurs from period to period. Because of this, investors usually consider the geometric mean a more accurate measure of returns than the arithmetic mean.

• An arithmetic average is the sum of a series of numbers divided by the count of that series of numbers.
• The geometric mean for a series of numbers is calculated by taking the product of these numbers and raising it to the inverse of the length of the series.