The sum of the deviations of a set of n numbers x₁, x₂, x₃, ..., xₙ measured from 15 is −90 and the sum of the deviations of the same numbers measured from −3 is 54. What is the arithmetic mean?

Let the sum of n numbers be S. From the first condition: Σ(xᵢ − 15) = S − 15n = −90. From the second: Σ(xᵢ − (−3)) = S + 3n = 54. Subtracting the first from the second: 18n = 144, so n = 8. Then S = 54 − 3(8) = 54 − 24 = 30. Arithmetic mean = S/n = 30/8 = 3·75.