When studying phenomena such as inflation or population changes that involve periodic increases or decreases, the geometric mean is used to find the average change over the entire period under study. To calculate the geometric mean of a sequence of $n$ values $x_{1}, x_{2}, \ldots, x_{n}$, we multiply them together and then find the $n$ th root of this product. Thus
$$
\text { Geometric mean }=\sqrt[n]{x_{1} \cdot x_{2} \cdot x_{3} \cdot \ldots \cdot x_{n}}
$$
Suppose that the inflation rates for the last five years are $4 \%, 3 \%, 5 \%, 6 \%$, and $8 \%$, respectively. Thus at the end of the first year, the price index will be $1.04$ times the price index at the beginning of the year, and so on. Find the mean rate of inflation over the 5 -year period by finding the geometric mean of the data set $1.04,1.03,1.05,1.06$, and $1.08 .$ (Hint: Here, $n=5, x_{1}=1.04, x_{2}=1.03$, and so on. Use the $x^{1 / n}$ key on your calculator to find the fifth root. Note that the mean inflation rate will be obtained by subtracting 1 from the geometric mean.)