Harmonic mean H.M. = n / (Σ(1/xi)). For two values: H.M. = 2ab/(a+b). Applications: Average speed, average rates. Example: Car travels 100 km at 50 km/h, returns 100 km at 100 km/h. Average speed = 2×100/(100 + 100) ÷ (50 + 100)... Correctly: Total distance = 200, time₁ = 2 hrs, time₂ = 1 hr, total time = 3 hrs. Average = 200/3 ≈ 66.7 km/h. Or using H.M.: (50 + 100)/2 = 75 (incorrect - harmonic). H.M. = 2×50×100/(50+100) = 10000/150 ≈ 66.7 (correct). Solving: Use formula; apply to rate problems. Advantage: Correct for averaging rates. Disadvantage: Affected by small values. Exam tip: Use when averaging rates/speeds. Remember: H.M. ≤ G.M. ≤ A.M.