We calculate the mean power spectrum of galaxies using published power spectra of galaxies and clusters of galaxies. On intermediate and small scales the mean power spectrum is closest to that derived from the 2-dimensional distribution of APM galaxies. This sample is not influenced by redshift distortions and is the largest and deepest sample of galaxies available. On large scales we use power spectra derived from 3-dimensional data for various galaxy populations and clusters which are reduced in amplitude to the power spectrum of APM galaxies. We analyze power spectra and find that available data indicate the presence of two different populations in the local Universe. Samples of clusters of galaxies as well as the APM 3-D, IRAS QDOT, and SSRS+CfA2 galaxy surveys cover relatively large regions in the Universe where rich, medium and poor superclusters are well represented. The mean power spectrum of these samples has a relatively sharp maximum at wavenumber k=0.05 +/- 0.01 h Mpc, followed by an almost exact power-law spectrum of index n approximately -1.9 toward smaller scales. The power spectrum found from LCRS data represents regions of the Universe with medium-rich and poor superclusters; it is flatter around the maximum. We argue that the peaked power spectrum probably corresponds to a fair sample of the Universe.

We suggest a new method to determine the bias parameter of galaxies relative to mass. The method is based on the assumption that the galaxy formation is a threshold process: in low-density local environment (voids) galaxies do not form. This assumption is supported by hydrodynamical simulations of galaxy formation. We compare of the distribution of particles in voids, medium- and high-density regions of numerical models. We investigate the influence of the biasing as a threshold effect to power spectra of galaxies and matter. We show that biasing is a linear phenomenon, i.e. the power spectrum of galaxies is similar to the power spectrum of mass, the difference in amplitudes of spectra depends on the fraction of total matter assigned to galaxies, F_gal. The fraction of mass in galaxies in the present epoch can be found using the calibration through the sigma₈ parameter. Applying estimates of these parameters given in Paper III we find for the biasing factor of galaxies relative to mass the value b_gal =1.3 +/- 0.1.

We suggest a new method to find sigma₈, the rms mass fluctuations in a top-hat sphere of radius 8h^-1 Mpc. The method is based on an integration of the mean power spectrum of galaxies, which is then reduced to the power spectrum of the mass using a simple relation between them in the linear regime based on the fraction of mass in galaxies. This relation is determined from detailed modelling of void evacuation for various cosmological models. Void evacuation depends on the density parameter of the Universe; the dependence is, however, significantly weaker than using the abundance of clusters of galaxies and arguments from Press-Schechter theory. We find sigma₈=0.89 +/- 0.05 for galaxies, and sigma₈ = 0.68 +/- 0.06 for mass.

All papers Ap. J., in press