Xe-129 gas-to-solution NMR chemical shifts for xenon dissolved in pure n-alkanes, n-alkyl alcohols, n-alkyl carboxylic acids, di-n-alkyl ketones, and cycloalkanes and in solutions of lauric acid in n-heptane are reported. The medium effect corrected for solvent density is found to be linearly dependent on the number of carbon atoms except for the shortest members of the series of linear solvents. The same slope is observed for all the linear solvents; the slope for the cycloalkanes is significantly different. These results are interpreted on the basis of a group contribution analysis. The relative contribution of methyl and methylene groups in linear solvents is found to be in very good agreement with the relative Xe-CH3 and Xe-CH2 dispersive interaction energies. The Xe-129 chemical shifts for solutions of lauric acid in n-heptane calculated from the group contributions are in excellent agreement with the experimental values. The deshielding effect of the methylene group in cycloalkanes and the Xe-129 chemical shift measured in the shortest members of the linear series of solvent are discussed in terms of intermolecular shielding functions and distributions of groups in the solvation shell of the Xe atom.