ρ(B) = ρ(A), and ξ(B) < = ξ(A), with ξ(B) = ξ(A) fif σ(A) = σ(B) – this is what averaging is all about, where ρ is the measure of the aspect of interest (e.g., area), ξ is the measure of the complexity of the object, and σ gives the contour (shape) of the object – for example, let A be a rectangle having length 4 and width 1 and B a square having side-length 2, and the aspect of interest be area.
[arithmetic mean]
[geometric mean]
[harmonic mean]
[power mean]