Individual and group loudness relations were obtained at a frequency in the region of impaired hearing for 100 people, 98 with bilateral cochlear impairment. Slope distributions were determined from absolute magnitude estimation (AME) and absolute magnitude production (AMP) of loudness; they were also derived from cross‐modality matching (CMM) and AME of apparent length. With respect to both the means and the individual slope values, the two distributions closely agree. More than half of the measured deviations are less than 20%, with an overall average of −1.5%, meaning that transitivity is preserved for bilaterally impaired individuals. Moreover, over the stimulus range where cochlear impairment steepens the loudness function, both the group means and the individual slope values are clearly larger than in normal hearing. The results also show that, for groups of people with approximately similar losses, the standard deviation is a nearly constant proportion of the mean slope value giving a coefficient of variation of about 27% in normal and impaired hearing. This indicates, in accord with loudness matching, that the size of the slopes depends directly on the degree of hearing loss. The results disclose that loudness measurements obtained by magnitude scaling are able to reveal the operating characteristic of the ear for individuals.