Step-by-Step Solution
Key Concept: The harmonic mean is the reciprocal of the arithmetic mean of reciprocals: HM = n / (1/a₁ + 1/a₂ + ... + 1/aₙ). For three numbers, HM = 3 / (1/4 + 1/8 + 1/16).
<p><strong>Step 1:</strong> Write the harmonic mean formula for n numbers:<br/>HM = n / (1/a₁ + 1/a₂ + ... + 1/aₙ)</p><p><strong>Step 2:</strong> For the numbers 4, 8, 16, identify n = 3</p><p><strong>Step 3:</strong> Calculate the sum of reciprocals:<br/>1/4 + 1/8 + 1/16 = 4/16 + 2/16 + 1/16 = 7/16</p><p><strong>Step 4:</strong> Apply the harmonic mean formula:<br/>HM = 3 ÷ (7/16) = 3 × 16/7 = 48/7 ≈ 6.857</p><p>∴ Answer: C (48/7 or approximately 6.86)</p>
Correct Answer: C