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 when you need to find the average rate of growth or the average of multiplicative quantities. It is calculated by taking the nth root of the product of all values.

Answer 1

The Correct Option is C

Topic: Measures of Central Tendency
Understanding the Question: Calculate the Geometric Mean (GM) for the set $\{2, 4, 8\}$.
Key Formulas and Approach: The Geometric Mean of $n$ numbers is the $n$-th root of their product: \[ GM = \sqrt[n]{x_1 \cdot x_2 \cdot \dots \cdot x_n} \] Detailed Solution:
Step 1: Identify the values. $n = 3$. The values are $x_1 = 2$, $x_2 = 4$, and $x_3 = 8$.
Step 2: Multiply the values. \[ \text{Product} = 2 \times 4 \times 8 = 64 \] Step 3: Take the n-th root. Since there are 3 numbers, we take the cube root: \[ GM = \sqrt[3]{64} \] Step 4: Simplify. Since $4^3 = 64$, the cube root is 4.
Conclusion: The Geometric Mean is 4.