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We present a micro-gravity experimental study of the statistical properties of intermediate number density vibro-fluidized inelastic spheres in a rectangular container. It is found that although when taking all the particles into account, the probability distributions of velocities both along and perpendicular to the vibration direction are exponential and symmetric, when dividing particles along the vibration direction into different bins, the local velocity distributions are found to deviate measurably from a symmetric distribution for the velocity component in the vibrating direction. The skewness analysis of the local distribution profiles for vx and vy shows that the local distribution of vx remains symmetric, however, the skewness of the distribution profile in vy changes nearly linear from positive to negative with skew = 0 near the center bin. This indicates a long range boundary effect of the asymmetry in vy. We further studied the hydrodynamic profiles granular pressure px and py, and temperature Tx and Ty in positive and negative components such as p+x and p−x, and Tx+ and Tx−, in accordance with the sign of velocity components. The profiles for the two components are found different along the y direction. Along vibration direction granular medium is found inhomogeneous and anisotropic not only in the particle number densities, but also in vy, py and Ty. This suggests new hydrodynamical modeling is needed for such vibro-fluidized granular systems.