n numbers x₁, x₂, x₃, …, xₙ of a set have the sum of deviations measured from 15 as -90 and the sum of deviations measured from -3 as 54. What is the arithmetic mean?

Sum of deviations from 15: Σ(xᵢ - 15) = -90, so Σxᵢ = 15n - 90. Sum of deviations from -3: Σ(xᵢ + 3) = 54, so Σxᵢ = 54 - 3n. Equating: 15n - 90 = 54 - 3n, so 18n = 144, n = 8. Then Σxᵢ = 15(8) - 90 = 30. Mean = 30/8 = 3.75. Wait — check: 54 - 3(8) = 54 - 24 = 30. ✓ Mean = 30/8 = 3.75.