In this work, we report multi-band flux variability and correlations of the nearby (z=0.031) blazar Markarian 421 (Mrk~421) using multi-wavelength (MWL) data from November 2014 to June 2016. In this period, Mrk~421 exhibited historically low activity in X-rays and very-high-energy gamma rays (VHE; E$>$0.1 TeV) and an additional spectral component was observed by \textit{Swift}-BAT. The highest flux variability occurs in X-rays and VHE which, despite the low activity, show a significant positive correlation with no time lag. The hardness ratios in the X-rays and VHE $\gamma$-rays show the "harder-when-brighter" trend observed in many blazars. Interestingly, the trend flattens at the highest fluxes, which suggests different processes dominating the brightest states. Enlarging our data set with data from the years 2007 to 2014, we measured a positive correlation between the optical and GeV emission centered at zero time lag, and a positive correlation between the optical/GeV and the radio emission over a range of about 60 days centered at a time lag of 43+9/-6 days. This observation is consistent with the radio-bright zone being located about 0.2 parsec downstream from the optical/GeV emission regions. In most of the energy bands, the flux distribution follows the Lognormal, rather than the Normal function, indicating that the variability may be dominated by a multiplicative process.