  Jet quenching, i.e. the suppression of high transverse momentum P_T hadron
production in ultrarelativistic heavy-ion collisions is among the most striking
experimental signatures of bulk medium formation. Efforts with the aim of
extracting quantitative information about the bulk medium from the measured
suppression mainly focus on the extraction of an averaged transport coefficient
<qhat> as a measure of the medium jet quenching power, with the underlying
assumption that <qhat> is a meaningful quantity to make comparisons both among
different models and between models and data. In this note, the main
uncertainties associated with the extraction of <qhat> from model fits to data
are briefly reviewed before the notion of an average transport coefficient
itself is investigated. It is shown in a case study that the choice of a
meaningful average is far from unique and that different well-motivated
definitions of averages lead not only to differences in the outcome of about a
factor four, but also in a different change of <qhat> with collision
centrality. This casts some doubt on the idea that condensing the information
about jet-medium interactions into a single average parameter is a meaningful
procedure.
