  We compile experimental data for the averaged transverse momentum
($\left\langle p_{T}\right\rangle $) of proton, $\Lambda$, $\Xi^{-}$,
$\Omega^{-}$ and $\phi$ at mid-rapidity in Au+Au collisions at $\sqrt{s_{NN}}=$
200, 39, 27, 19.6, 11.5, 7.7 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}=$
2.76 TeV, and find that experimental data of these hadrons exhibit systematic
correlations. We apply a quark combination model with equal-velocity
combination approximation to derive analytic formulas of hadronic $\left\langle
p_{T}\right\rangle $ in the case of exponential form of quark $p_{T}$ spectra
at hadronization. We use them to successfully explain the systematic
correlations exhibited in $\left\langle p_{T}\right\rangle $ data of
$p\Lambda$, $\Lambda\Xi^{-}$, $\Xi^{-}\Omega^{-}$ and $\Xi^{-}\phi$ pairs. We
also use them to successfully explain the regularity observed in $\left\langle
p_{T}\right\rangle $ of these hadrons as the function of
$(dN_{ch}/dy)/(N_{part}/2)$ at mid-rapidity in central heavy-ion collisions at
both RHIC and LHC energies. Our results suggest that the constituent quark
degrees of freedom and the equal-velocity combination of these constituent
quarks at hadronization play important role in understanding the production of
baryons and $\phi$ meson at these RHIC and LHC energies.
