  We analyze how predictions of cosmological models depend on a choice of
described observational data, restrictions on flatness,
  and how this choice can alleviate the $H_0$ tension. These effects are
demonstrated in the $w$CDM model in comparison with the standard $\Lambda$CDM
model. We describe the Pantheon sample observations of Type Ia supernovae, 31
Hubble parameter data points $H(z)$ from cosmic chronometers, the extended
sample with 57 $H(z)$ data points and observational manifestations of cosmic
microwave background radiation (CMB).
  For the $w$CDM and $\Lambda$CDM models in the flat case and with spatial
curvature we calculate $\chi^2$ functions for all observed data in different
combinations, estimate optimal values of model parameters and their expected
intervals. For both considered models the results essentially depend on a
choice of data sets. In particular, for the $w$CDM model with $H(z)$ data,
supernovae and CMB the $1\sigma$ estimations may vary from
$H_0=67.52^{+0.96}_{-0.95}$ km\,/(s$\cdot$Mpc) (for all $N_H=57$ Hubble
parameter data points) up to $H_0=70.87^{+1.63}_{-1.62}$ km\,/(s$\cdot$Mpc) for
the flat case ($k=0$) and $N_H=31$. These results might be a hint how to
alleviate the problem of $H_0$ tension: different estimates of the Hubble
constant may be connected with filters and a choice of observational data.
