Calculate the geometric mean of the set of data 6, 8, 12

Question

ScanSolve AI Tutor · Accepted Answer

The problem asks to calculate the Geometric Mean (GM) for the given set of data. The definition provided states that the Geometric Mean is the $n^{\text{th}}$ root of the product of the numbers. The formula for the Geometric Mean is $\text{GM} = \sqrt[n]{x_1 \times x_2 \times \dots \times x_n}$ .

Identify the given numbers and the count.
The numbers are $x = \{6, 8, 12\}$ .
The count of numbers is $n = 3$ .
Multiply the numbers together.
$\text{Product} = 6 \times 8 \times 12$
Calculate the product.
$\text{Product} = 48 \times 12 = 576$
Apply the Geometric Mean formula.
Since there are 3 numbers, we need to find the cube root of their product.
$\text{GM} = \sqrt[3]{576}$
Calculate the cube root.
$\text{GM} \approx 8.320$
The Geometric Mean for the given set of numbers is:
$8.320$

Calculate the geometric mean of the set of data 6, 8, 12

Answer

Step-by-step solution

Identify the given numbers and the count.

Multiply the numbers together.

Calculate the product.

Apply the Geometric Mean formula.

Calculate the cube root.

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