B2 Geometric Mean Review Revised

The geometric mean of two numbers a and b is given by the formula: $$\text{Geometric Mean} = \text{sqrt}(a \times b)$$ .

The geometric mean of three numbers a, b, and c is calculated as: $$\text{Geometric Mean} = \text{sqrt[3]}(a \times b \times c)$$ .

The geometric mean is $$\text{sqrt}(4 \times 16) = \text{sqrt}(64) = 8$$ .

The arithmetic mean is always greater than or equal to the geometric mean for non-negative numbers.

The geometric mean is used to calculate average rates of return over time, especially when dealing with percentages.

Using the formula: $$\text{sqrt}(x \times 25) = 15$$ , we find that $$x = 15^2 / 25 = 9$$ .

The geometric mean of n numbers is given by: $$\text{Geometric Mean} = \text{sqrt[n]}(x_1 \times x_2 \times ... \times x_n)$$ .

Multiply all the values together and then take the nth root, where n is the number of values.

The geometric mean is $$\text{sqrt[3]}(1 \times 3 \times 9) = \text{sqrt[3]}(27) = 3$$ .

The geometric mean is preferred when dealing with ratios, percentages, or values that are multiplicative in nature.