Question

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 nth root of the product of the numbers. For example, the geometric mean of 4, 5, and 6 is G.M. = (4 · 5 · 6)1/3 = 3 120 ≈ 4.9.

(a) Find the arithmetic and geometric means for the numbers 2, 3, 6, 7, 7, 8, and 10. (Round your answers to one decimal place.) arithmetic mean Incorrect: Your answer is incorrect. geometric mean Incorrect: Your answer is incorrect.
(b) The growth rates for three cities are 1.7%, 2.2%, and 0.9%. Compare the arithmetic and geometric means. (Round your answers to two decimal places.)

Answer 1

Answer:a) A.M= 6.1 G.M= 5.4

b) A.M = 1.6% G.M= 1.5%

Explanation:

Arithmetic mean = sum of data given/ number of data given

Geometric mean = nth root of the product of n data

Where n is the number of data given.

a) A.M = (2+3+6+7+7+8+10)/7 = 6.1

G.M = (2×3×6×7×7×8×10)^(1/7) = 5.4

b) A.M = (1.7+2.2+0.9)/3 = 4.8/3 = 1.6%

G.M= (1.7×2.2×0.9)^(1/3) = 1.5%

G.M is relatively lower than the A.M.