The geometric mean (GM) is defined as the nth root of the product of n values. The

Chapter 3, Problem 40

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The geometric mean (GM) is defined as the nth root of the product of n values. The formula is The geometric mean of 4 and 16 is The geometric mean of 1, 3, and 9 is The geometric mean is useful in finding the average of percentages, ratios, indexes, or growth rates. For example, if a person receives a 20% raise after 1 year of service and a 10% raise after the second year of service, the average percentage raise per year is not 15 but 14.89%, as shown. GM 1.21.1 1.1489 GM 3 139 3 27 3 GM 416 64 8 GM n X1X2X3LXn 2 140 150 44.44 distance time 200 4.5 44.44 2 100 50 2 1 100 40 2.5 HM 4 11 14 15 12 2.05 or His salary is 120% at the end of the first year and 110% at the end of the second year. This is equivalent to an average of 14.89%, since 114.89% 100% 14.89%. This answer can also be shown by assuming that the person makes $10,000 to start and receives two raises of 20 and 10%. Raise 1 10,000 20% $2000 Raise 2 12,000 10% $1200 His total salary raise is $3200. This total is equivalent to $10,000 14.89% $1489.00 $11,489 14.89% 1710.71 $3199.71 $3200 Find the geometric mean of each of these. a. The growth rates of the Living Life Insurance Corporation for the past 3 years were 35, 24, and 18%. b. A person received these percentage raises in salary over a 4-year period: 8, 6, 4, and 5%. c. A stock increased each year for 5 years at these percentages: 10, 8, 12, 9, and 3%. d. The price increases, in percentages, for the cost of food in a specific geographic region for the past 3 years were 1, 3, and 5.5%. 41. A useful mean in the physical sciences (su