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 defined as the square root of their product: √(a*b).

Front

How is the geometric mean used in statistics?

Back

The geometric mean is used to calculate average rates of return in finance and to find central tendency in skewed distributions.

Front

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

Back

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

Front

When is the geometric mean preferred over the arithmetic mean?

Back

The geometric mean is preferred when dealing with multiplicative processes or when the data is skewed.

Front

Calculate the geometric mean of 4 and 16.

Back

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

Front

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

Back

The geometric mean is always greater than or equal to the harmonic mean for a given set of positive numbers.

Front

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

Back

Let the other number be x. Then √(5*x) = 10, so x = 40.

Front

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

Back

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

Front

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

Back

The geometric mean is used to calculate average growth rates over time, especially in finance.

Front

What is the geometric mean of the numbers 2, 8, and 18?

Back

The geometric mean is (2*8*18)^(1/3) = 6.