Applying the Markov chain Monte Carlo algorithm and using low-redshift observational data, we put cosmological constraints on dark energy cosmologies. Our main aim is to show the influence of each data sample on the procedure of constraining. The main results of our analysis are as follows. In the case of the Pantheon catalog of supernovae, one can put approximately three times tighter constraints on the cosmological parameters compare to the early Gold dataset. Combining the Pantheon with the Hubble data, we obtain ∼ 1.5 times tighter constraints compare to the Pantheon solely. We show that in cluster scale due to low growth rate data with large error bars, one cannot put tight constraints on the cosmological parameters. Combining the expansion and growth rate data leads to tighter constraints on the cosmological parameters. While the local value of Hubble constant H0 has a ∼ 3.4σ tension with Planck inferred result, we show that by combining the expansion and growth data with local H0 data, the tension is alleviated to a 1.7σ. Finally, jointing the Pantheon, Hubble data, growth rate, H0 with the BAO measurements gets roughly 7 − 8% tighter constraints on the matter density and Hubble constant parameters.
