Geometric Mean

Front

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

Back

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

Front

How do you find the geometric mean of three numbers a, b, and c?

Back

The geometric mean of three numbers is the cube root of the product: (a * b * c)^(1/3).

Front

What is the formula for the geometric mean of n numbers?

Back

The geometric mean of n numbers is (x1 * x2 * ... * xn)^(1/n).

Front

If the lengths of two sides of a right triangle are 3 and 4, what is the geometric mean of these lengths?

Back

The geometric mean is √(3 * 4) = √12 = 2√3.

Front

In a geometric sequence, if the first term is 2 and the second term is 8, what is the geometric mean?

Back

The geometric mean is √(2 * 8) = √16 = 4.

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 for non-negative numbers.

Front

How can the geometric mean be used in finance?

Back

The geometric mean is used to calculate average rates of return over time, especially for investments.

Front

If the geometric mean of two numbers is 10 and one of the numbers is 5, what is the other number?

Back

The other number is 20, since √(5 * x) = 10 leads to x = 20.

Front

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

Back

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

Front

How do you calculate the geometric mean of a set of data?

Back

Multiply all the data points together and take the nth root, where n is the number of data points.