Geometric Mean Practice

Front

What is the geometric mean of two numbers?

Back

The geometric mean of two numbers a and b is the square root of their product, calculated as √(a * b).

Front

How do you calculate the geometric mean of three numbers?

Back

To calculate the geometric mean of three numbers a, b, and c, use the formula: (a * b * c)^(1/3).

Front

What is the geometric mean of 4 and 16?

Back

The geometric mean of 4 and 16 is √(4 * 16) = √64 = 8.

Front

Why is the geometric mean used in finance?

Back

The geometric mean is used in finance to calculate average rates of return over time, as it accounts for compounding.

Front

What is the relationship between the arithmetic mean and the geometric mean?

Back

The arithmetic mean is always greater than or equal to the geometric mean for non-negative numbers, known as the AM-GM inequality.

Front

How do you find the geometric mean of a set of numbers?

Back

To find the geometric mean of a set of n numbers, multiply all the numbers together and take the n-th root of the product.

Front

What is the geometric mean of 1, 3, and 9?

Back

The geometric mean of 1, 3, and 9 is (1 * 3 * 9)^(1/3) = 3.

Front

In what situations is the geometric mean preferred over the arithmetic mean?

Back

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

Front

What is the geometric mean of 2, 8, and 32?

Back

The geometric mean of 2, 8, and 32 is (2 * 8 * 32)^(1/3) = 8.

Front

How does the geometric mean relate to the concept of growth rates?

Back

The geometric mean is used to calculate average growth rates, as it provides a more accurate measure when growth is compounded.