  The blazar Mrk 421 is one of the closest, brightest and fastest varying
source in the extragalactic X-ray/TeV sky. In the last years, many
multi-wavelength campaigns have been carried out to study the correlation
between the very high energy (VHE) $\gamma$-ray and X-ray fluxes of this source
and, although the activity in these two energy ranges seems to be correlated in
many observations, no conclusive results have been achieved yet. In this work
we present a robust study of the VHE $\gamma$-ray/X-ray correlation of Mrk 421
with data taken with different VHE experiments on different time scales and for
different levels of activity of the source, with special focus on the low
activity states. In particular, we discuss the robustness of the correlation at
the lowest fluxes corresponding to the quiescent state of Mrk 421.
