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Using a set of hydrodynamical simulations of 62 galaxy clusters and groups westudy the ICM of inhomogeneities, focusing on the ones on the large scale that,unlike clumps, are the most difficult to identify. To this purpose we introducethe concept of residual clumpiness, C_R, that quantifies the large-scaleinhomogeneity of the ICM. After showing that this quantity can be robustlydefined for relaxed systems, we characterize how it varies with radius, massand dynamical state of the halo. Most importantly, we observe that itintroduces an overestimate in the determination of the density profile from theX-ray emission, which translates into a systematic overestimate of 6 (12)% inthe measurement of M_gas at R_200 for our relaxed (perturbed) cluster sample.At the same time, the increase of C_R with radius introduces also a ~2%systematic underestimate in the measurement of the hydrostatic-equilibrium mass(M_he), which adds to the previous one generating a systematic ~8.5%overestimate in f_gas in our relaxed sample. Since the residual clumpiness ofthe ICM is not directly observable, we study its correlation with the azimuthalscatter in the X-ray surface brightness of the halo and in the y-parameterprofiles. We find that their correlation is highly significant (r_S = 0.6-0.7),allowing to define the azimuthal scatter measured in the X-ray surfacebrightness profile and in the y-parameter as robust proxies of C_R. Afterproviding a function that connects the two quantities, we obtain thatcorrecting the observed gas density profiles using the azimuthal scattereliminates the bias in the measurement of M_gas for relaxed objects, whichbecomes (0+/-2)% up to 2R_200, and reduces it by a factor of 3 for perturbedones. This method allows also to eliminate the systematics on the measurementsof M_he and f_gas, although a significant halo to halo scatter remains.(abridged)

Large-scale inhomogeneities of the intracluster medium: improving mass estimates using the observed azimuthal scatter