The QCD theory predicts existence of glueballs, but so far all experimental endeavor fails to identify any of such states. To remedy the obvious discrepancy between the QCD which is proved to be a successful theory for strong interaction and the failure of experimentally searching for glueballs, one is tempted to accept the most favorable interpretation that the glueballs mix with regular $q\bar q$ states of the same quantum numbers... The lattice estimate on the masses of the pure $0^{++}$ glueballs ranges from 1 to 2 GeV which is the region of the $f_0$ family. Thus many authors suggest that the $f_0$ mesonic series is an ideal place to study possible mixtures of glueballs and $q\bar q$. In this paper following the strategy proposed by Close, Farrar and Li, we try to determine the fraction of glueball components in $f_0$ mesons using the measured branching ratios of $J/\psi$ radiative decays into $f_0$ mesons. Since the pioneer papers by Close et al. more than 20 years elapsed and more accurate measurements have been done by several experimental collaborations, so that based on the new data, it is time to revisit this interesting topic. Our numerical results show that $f_0(500)$, $f_0(980)$, are almost pure quark anti-quark bound states, while for $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, to fit both the experimental data of $J/\psi$ radiative decay and their mass spectra, glueball components are needed. Moreover, the mass of the pure $0^{++}$ glueball is phenomenologically determined. (read more)