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 x1, x2,..., xn, we multiply them together and then find the nth root of this product. Thus

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, x1 = 1.04 = x2 = 1.03, and so on. Use the x1/n key on your calculator to find the fifth root. The mean inflation rate will be obtained by subtracting 1 from the geometric mean.)

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Geometric mean = exi X2 · ·X3· .