The summary of results of numerous investigations obtained by various authors from observations indicate that the distribution of the mean number density of quasars n_QSO over the redshift z is nonmonotonic and has the maximum at z ≈ 2.2...2.5. We show that such character of the distribution n_QSO(z) finds its explanation in the framework of standard cosmological scenario for large scale structure formation from primordial matter density fluctuations under the influence of the gravitational instability, in cosmological model with the energy density of vacuum Ω_Λ ≈ 0.7 and matter density Ω_M ≈ 0.3. In this case quasars are considered as an early short stage in the evolution of massive galaxies with the mass M ∼ (1...3)⋅10¹¹ M_☉.