About Harmonic Mean

The harmonic mean is a type of average that is particularly useful when dealing with rates, ratios, or when the average of reciprocals is needed. It's calculated as the reciprocal of the arithmetic mean of the reciprocals of the numbers.

Formula:

For a set of numbers x₁, x₂, ..., xₙ, the harmonic mean is:

HM = n / (1/x₁ + 1/x₂ + ... + 1/xₙ)

Example:

For numbers 2, 4, 8:

HM = 3 / (1/2 + 1/4 + 1/8) = 3 / (0.5 + 0.25 + 0.125) = 3 / 0.875 = 3.4286

Common Applications:

• Average speed calculations
• Financial ratios
• Electrical resistance in parallel circuits
• Price-to-earnings ratios