This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI 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^th root of the product of the numbers. The formula for the Geometric Mean is GM = [n]x_1 × x_2 × × x_n. Step 1: Identify the given numbers and the count. The numbers are x = \6, 8, 12\. The count of numbers is n = 3. Step 2: Multiply the numbers together. Product = 6 × 8 × 12 Step 3: Calculate the product. Product = 48 × 12 = 576 Step 4: Apply the Geometric Mean formula. Since there are 3 numbers, we need to find the cube root of their product. GM = [3]576 Step 5: Calculate the cube root. GM ≈ 8.320 The Geometric Mean for the given set of numbers is: 8.320 Last free one today — make it count tomorrow, or type /upgrade for unlimited.