  We prove that the minimal area of a holomorphic triangle whose boundary lies
on the union of any three Lagrangian submanifolds is bounded from above by the
Lagrangian spectral norm of any pair taken out of the three. We show a relation
between this result and the median quasi-state on the 2-sphere. The median
quasi-state gives rise to a measure of Poisson non-commutativity of any pair of
functions. We answer a question of Entov--Polterovich--Zapolsky by giving a
sharp upper bound on the ratio between this measure and the uniform norm of the
Poisson bracket of the pair. The sharpness of this bound also implies a lower
bound on the defect of the Calabi quasi-morphism.
