We report a characterization of the multiband flux variability and correlations of the nearby (z = 0.031) blazar Markarian 421 (Mrk 421) using data from Metsähovi, Swift, Fermi-LAT, MAGIC, FACT, and other collaborations and instruments from 2014 November till 2016 June. Mrk 421 did not show any prominent flaring activity, but exhibited periods of historically low activity above 1 TeV (F>1 TeV < 1.7 × 10-12 ph cm-2 s-1) and in the 2-10 keV (X-ray) band (F 2-10, keV< 3.6× 10-11 erg cm-2 s-1), during which the Swift-BAT data suggest an additional spectral component beyond the regular synchrotron emission. The highest flux variability occurs in X-rays and very high-energy (E > 0.1 TeV) γ-rays, which, despite the low activity, show a significant positive correlation with no time lag. The HRkeV and HRTeV show the harder-when-brighter trend observed in many blazars, but the trend flattens at the highest fluxes, which suggests a change in the processes dominating the blazar variability. Enlarging our data set with data from years 2007 to 2014, we measured a positive correlation between the optical and the GeV emission over a range of about 60 d centred at time lag zero, and a positive correlation between the optical/GeV and the radio emission over a range of about 60 d centred at a time lag of 43+9-6 d. This observation is consistent with the radio-bright zone being located about 0.2 parsec downstream from the optical/GeV emission regions of the jet. The flux distributions are better described with a lognormal function in most of the energy bands probed, indicating that the variability in Mrk 421 is likely produced by a multiplicative process.