The mean defined in the text is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the geometric mean (G.M.), is used in business and economics for finding average rates of change, average rates of growth, or average ratios. This mean is defined to be the \(n\)th root of the product of the numbers. For example, the geometric mean of 4,5 , and 6 is

\[\begin{aligned}\text { G.M. } & =(4 \cdot 5 \cdot 6)^{1 / 3} \\& =\sqrt[3]{120} \\& \approx 4.9\end{aligned}\]

a. Find the arithmetic and geometric means for the numbers 2 , \(3,5,7,7,8\), and 10 .

b. The growth rates for three cities are \(1.5 \%, 2.0 \%\), and \(0.9 \%\). Compare the arithmetic and geometric means.