the ISGMR centroid energy of $^{208}$Pb. In recent years, significant progress has been made in determining $L$ and its value is essentially consistent with $L=60\pm 30$ MeV depending on the observables and methods used in the studies [Mye96,Che05a,She07,Kli07,Tri08,Tsa09,Dan09,Cen09,Car10,XuC10,Liu10,Che11a]{}. Using $L=60\pm 30$ MeV, we can estimate an uncertainty of about $\pm 0.281$ MeV for the ISGMR centroid energy in $^{208}$Pb from Fig. \[XEaPb208\]. On the other hand, for the isoscalar effective mass, the empirical value of $m_{s,0}^{\ast }=(0.8\pm 0.1)m$ has been obtained from the analysis of both isoscalar quadrupole giant resonances data in doubly closed-shell nuclei and single-particle spectra [@Liu76; @Boh79; @Far97; @Rei99; @Les06]. From Fig. [XEaPb208]{}, we can obtain an uncertainty of about $\pm 0.382$ MeV for the ISGMR centroid energy in $^{208}$Pb using the empirical value of $m_{s,0}^{\ast }=(0.8\pm 0.1)m$. Assuming the two uncertainties due to the present uncertainties of $L$ and $m_{s,0}^{\ast }$ on the ISGMR centroid energy in $^{208}$Pb are independent, we thus can add them quadratically to obtain an uncertainty of about $\pm 0.474$ MeV for the ISGMR centroid energy in $^{208}$Pb. Then, using the approximate relation $(\delta K_{0}/K_{0})=2$($\delta E_{\mathrm{ISGMR}}$/$E_{\mathrm{ISGMR}}$) from Eq. (\[EGMRKa\]), we can obtain an uncertainty of $\pm 7\%$ for $K_{0}$ with $E_{\mathrm{ISGMR}}\approx 14$ 