Geometric Mean

Front

What is the geometric mean of two numbers a and b?

Back

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

Front

How do you calculate the geometric mean for n numbers?

Back

The geometric mean for n numbers is calculated as the n-th root of the product of the numbers: (x1 * x2 * ... * xn)^(1/n).

Front

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

Back

The geometric mean is always less than or equal to the arithmetic mean, except when all numbers are equal, in which case they are equal.

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 4 and 16?

Back

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

Front

If the geometric mean of two numbers is 10, what can you say about the product of those two numbers?

Back

The product of the two numbers is 10^2 = 100.

Front

How does the geometric mean apply in finance?

Back

In finance, the geometric mean is used to calculate average growth rates over time, such as compound interest.

Front

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

Back

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

Front

Can the geometric mean be used for negative numbers?

Back

No, the geometric mean cannot be calculated for negative numbers as it involves taking square roots.

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.