  We have obtained column density maps for an unbiased sample of 120 molecular
clouds in the third quadrant of the Milky Way mid-plane (b$\le |5|^{\circ}$)
within the galactic longitude range from 195$^{\circ}$ to 225$^{\circ}$, using
the high sensitivity $^{12}$CO and $^{13}$CO ($J=1-0$) data from the Milky Way
Imaging Scroll Painting (MWISP) project. The probability density functions of
the molecular hydrogen column density of the clouds, N-PDFs, are fitted with
both log-normal (LN) function and log-normal plus power-law (LN+PL) function.
The molecular clouds are classified into three categories according to their
shapes of N-PDFs, i.e., LN, LN+PL, and UN (unclear), respectively. About 72\%
of the molecular clouds fall into the LN category, while 18\% and 10\% into the
LN+PL and UN categories, respectively. A power-law scaling relation,
$\sigma_s\propto N_{H_2}^{0.44}$, exists between the width of the N-PDF,
$\sigma_s$, and the average column density, $N_{H_2}$, of the molecular clouds.
However, $\sigma_s$ shows no correlation with the mass of the clouds. A
correlation is found between the dispersion of normalized column density,
$\sigma_{N/\rm <N>}$, and the sonic Mach number, $\mathcal{M}$, of molecular
clouds. Overall, as predicted by numerical simulations, the N-PDFs of the
molecular clouds with active star formation activity tend to have N-PDFs with
power-law high-density tails.
