Question

What is the geometric mean of 2, 4, and 8?

• A. 4.67
• B. 3.43
• C. 4
• D. 4.5

Hint:

The geometric mean is useful for finding the average growth rate over time or for multiplying data points.

Answer 1

The Correct Option is B

Step 1: Formula for geometric mean.
The geometric mean of \( n \) values \( x_1, x_2, \dots, x_n \) is given by: \[ GM = \left( \prod_{i=1}^n x_i \right)^{\frac{1}{n}} \]

Step 2: Apply the formula.
For the values 2, 4, and 8, the geometric mean is: \[ GM = (2 \cdot 4 \cdot 8)^{\frac{1}{3}} \] \[ GM = (64)^{\frac{1}{3}} = 4 \]

Step 3: Conclusion.
The geometric mean of 2, 4, and 8 is 4, so the correct answer is (C).