Where to use geometric mean?

Answer 1

The geometric mean of two numbers is the square root of their product. So take 12 and 3, their product is 36 and the geometric mean is 6. If you have 3 numbers, take the cube root of the product. For n numbers take the nth root. The geometric mean is used when dealing with percentages and rates of change. Say the growth rate of companies where the rate is given as a percent. I am going to illustrate this with an example. A company growing annually by 2.5%, 3%, and 3.5%, profit in year 1 = 1.025 times profit in year 0 Profit in year 2 = 1.03 times profit in year 1 = 1.03 * 1.025 times profit in year 0 Profit in year 3 = 1.035 times profit in year 2 = 1.035 * 1.03 * 1.025 times profit in year 0 Thus the ratio of the profit in the third year to the profit in the base year is 1.025 * 1.03 * 1.035 If the growth rate had been the same each year, the ratio would be N * N * N For the growth over 3 years to be the same in both cases, we must have 1.025 * 1.03 * 1.035 = N * N * N The solution is N = (1.025 * 1.03 * 1.035)^(1/3) = 1.029992 That is, the cube root of the product of the annual growth factors. This is the geometric mean. (Example courtesy of Doctor Rick, The Math Forum)